Yes, these changes to the Way of the Four Elements subclass are balanced, but in my opinion, they don't quite go far enough and they don't help the monk feel like a monk

As it happens, I've finally gotten around to playtesting my own version of the new and improved Way of the Four Elements monk subclass, which is pretty much what this blog suggested but with a few extra features that I won't go into just yet.

See also, my previous questions relating to this subclass:

• Would the Four Elements monk be balanced with more disciplines and cantrips?
• Does the ki cost of Way of the Four Elements monk spells scale for higher level spells?

Specifically, I did two test runs, from level 3 to level 20, and in my first run I had ki costs as-is, and my second run I had the ki costs 1 point lower than RAW (rather than reducing by 2 as the blog suggests).

In both runs I had the monk learn two disciplines instead of one whenever they get to learn more (so 3rd, 6th, 11th and 17th level) and I added cantrips (the same ones I outlined in the first of my linked questions, since I didn't agree with that blog's suggestions; I mean, acid splash? How is that elemental considering the "four elements" theme of the elemental disciplines?), allowing a third cantrip to be chosen at 10th level (since all other classes and subclasses with access to cantrips do the same).

Ki point cost reduction

I found that (as other answers on various Q&As on this subject have pointed out before me) one of the main problems with this archetype is that the subclass features and the base class features are competing over the same resource pool; ki points.

I found that, during my first run, using disciplines like Water Whip, even at Tier 1 play, used up my ki so fast that I'd be completely out of resources for the rest of the encounter, and the next one too if we weren't going to short rest; this denied me Flurry of Blows or other ki features. At Tier 2 play it would deny me Stunning Strike as well, and the problem now gets worse because I can "upcast" my disciplines, eating through even more ki points.

I know that other classes have finite resources too (i.e. spell slots), but the amount of ki is less overall; if we compare ki to spell slots, the best comparison is to use the Variant: Spell Points optional rule from the DMG (pp. 288-289). Reviewing the table of conversion on p. 288, we can see that the number of spell points even a half caster would have quickly outpaces the ki points that a monk has.

At level 3, a monk has 3 ki, whereas a ranger or paladin would have 6. And it only gets worse once we reach level 5, where a ranger or paladin would have 14 but a monk is still only at 5. Eldritch Knights and Arcane Tricksters are more on par, with only 4 spell points at level 3, and 6 spell points between levels 4-6, which roughly matches the monk, but then they quickly outpace the monk again once they gain access to 2nd level spell slots at 7th level.

The obvious counterargument is "but monks get their ki points back on a short rest", which is more comparable to a warlock, the only other class that gets all their spell slots/points back on a short rest. However, even they have a greater selection of spells, and they automatically upcast, whereas the monk doesn't (they have to sink yet more ki into the spell to do that), and warlocks still have other things they can do, such as make use of eldritch invocations and limited subclass abilities, whereas monks are denied their other defining features such as Flurry of Blows and Stunning Strike.

Reducing the ki points by 1 (except for Fangs of the Fire Snake, which already only costs 1 ki) helps with all of that, because, although it allows them to cast more often, this is also replacing their melee attacks, which is what monks are "supposed" to be about, and it is still denying them the chance to Stunning Strike, etc, since they are still sharing the same resource pool, even if the disciplines are now less resource-hungry.

Reducing the ki by a further point as the blog suggests might allow for these spells to be even less resource-hungry, but I think keeping it to 1 less helps to keep things more intuitive, especially when it comes to upcasting. I went with "ki point cost = spell slot level", so Fist of Four Thunders to cast thunderwave costs 1 ki at base level, and if you "upcast" it to 2nd level, it now costs 2 ki points. So 2nd level = 2 ki. That's more intuitive.

I can see what the blog was suggesting with making the disciplines even "cheaper" by reducing by 2, but I feel like there are other ways that the monk can make up the difference without making all of their spell super-cheap. See below in my "Other Changes" section for more on this (in short, a monk is still a monk, so they should do more monk stuff rather than trying to force them to be a subpar caster solely using the monk class framework).

Number of Disciplines

As András' answer to one of my above questions points out, the number isn't too important, because the main thing that hampers Way of the Four Elements monks (besides the fact that everything uses the same resource pool) is that they must cast a spell or attack, and making many attacks is what the monk class is supposed to be all about.

That said, I found that even with learning two disciplines where RAW you would learn one, I was still sometimes wishing I'd picked others in certain situations. I found that it still adds versatility but without making it "overpowered" (indeed, András mentions how they gave their monk all of the disciplines, and it still wasn't enough to make them overpowered).

I will point out, however, that I've made many more homebrew disciplines that give access to any elemental-themed spell, such as erupting earth, flaming sphere, tidal wave, wind wall, etc, as outlined in the second of my linked questions above, but this didn't make too much difference because you still only have two, then four, then six, etc. It's still a very small number of spells even when compared to something like a sorcerer or warlock, but I would be wary of having them learn more than two when RAW they would learn one.

... and can replace any discipline you know with another one that you meet the level requirements to learn when you gain a level in this class.

I didn't personally ever use this, but I believe this is sensible, since that's what other casters can do, such as sorcerers, warlocks, rangers, etc. I have no idea why Way of the Four Elements monks are forced to wait until level 6 to swap out a spell they learned at level 3, etc. That's not how any other spellcasting class (that "just knows" their spells) works.

Cantrips

I used a slightly different list of cantrips, as outlined in my first linked question above: control flames, frostbite, gust, mold earth, produce flame, ray of frost, shape water and thunderclap. However, there's a lot of crossover, and I again didn't find that this had much impact beyond giving the monk a ranged option when they needed it. And stuff like gust and shape water isn't useful in combat anyway so hardly matters.

Regarding their use in combat, the damage is still worse than what they'd be doing with their unarmed strike (even if you ignore the bonus action attacks), since at Tier 2, 2d6 + 6 (if we assume DEX of 16) is better than 2d8 (from produce flame or ray of frost), and at Tier 3, 2d8 + 8 (now assuming DEX of 18) is still better than 3d8. At Tier 4 it becomes 2d10 + 10 (now assuming DEX of 20), which is still better than 4d8, so the cantrip's main benefit is gaining a ranged attack, not outdoing the normal melee damage that a monk can do.

However, where the blog says:

When you gain a level in this class, you can replace one of these cantrips with another instead of replacing an elemental discipline with another.

No, I didn't do that and wouldn't do that simply because no other class before the Artificer came out can swap out cantrips, even classes that let you swap out spells on level up. I don't like the idea of letting monks do this, but on the other hand, since the Artificer class lets you do this, there is now an official precedent set for allowing this, so if you want to, you can, but I personally wouldn't. With the Artificer, at least, the implication is that they are tweaking their technology to cast different cantrips, but other spellcaster classes don't because they actually had to learn how to cast their cantrip themselves, but that's just my opinion on flavour; mechanically, I don't see this being a huge issue either way.

Other changes

So, I mentioned that I added a few other features to my Way of the Four Elements revamp. Those features were:

• Can bonus action attack after casting spells at level 6;
• Can reduce and maybe return elemental damage at level 11, similar to Deflect Arrows;
• Can cast a big spell at level 17, but only once per long rest.

The trouble with this archetype is mainly that it's trying to turn the monk into a subpar caster, since they have fewer known spells (even with the "two disciplines instead of one" adjustment discussed above) and far fewer resources to spend on these spells (even if they get it back on short rests, that seems like little comfort in practice; or at least, that's what I found during my playtesting). A monk is supposed to be about martial arts, so the best way to do that is taking on one of András' suggestions; letting them make bonus action attacks after casting spells (and in my case, even cantrips).

Firstly, this doesn't compete with the monk's normal actions, because if they simply attack, they can do their bonus action stuff (Martial Arts or Flurry of Blows) anyway. This change simply allows them to still be a monk even when they're casting spells. I gave this at level 6 to match the pattern of certain combative bard and wizard subclasses getting Extra Attack at level 6, even though most classes get it at level 5.

I found that this gave the monk more versatility that casting spells takes away from them. Dragging an enemy over to you with Water Whip and then following that up with a punch to the face (optionally Flurry of Blows for two punches, optionally with Stunning Strike; remember, still eating through your very limited one-and-only resource pool) feels very cool, and helps the monk to "feel" like they're a magical monk, not a magician or a monk.

Reducing and returning elemental damage is more just because it's cool than necessary, but in practice it just gives another option to the monk to react to spells (since they can't cast shield or counterspell like a proper spellcaster can). Because functionally its the same as a combination of Deflect Missiles and absorb elements (in the sense that you reduce elemental damage and can use that damage against the enemy), and uses your reaction either way, this just feels more like a "cool trick" than something that impacts the balance in any meaningful way, but I thought to mention it anyway. Up to you whether you include this or not.

Finally, the "big spells", as per my second question above. I allowed the Way of the Four Elements monk to cast one big spell (still costs a load of ki to cast) once per long rest. Only once (comparable to a warlock's Mystic Arcanum), and they need to reach 17th level before they can even do that. If full casters can only cast a big spell once (although technically a 17th level full casters can cast a 6th level spell 4 times), I don't think a monk that is effectively a half-caster should be able to do so more than once.

Sure, a Way of the Four Elements monk at 17th level is now able to cast cone of cold (as long as they have the ki for it), but that's not as impressive at this level as it was when wizards were doing it at 9th level. I felt they needed something truly deserving of a 17th level feature when they hit Tier 4.

If I compare this to other subclasses:

• Quivering Palm; that only costs 3 ki points to do 10d10 on a successful save to a creature, and they can do this to many enemies, although not all at once like an AOE, as many times as they have ki to spend.
• Intoxicated Frenzy; a drunken monk can potentially hit and stun 7 enemies for 8 ki point (1 for Flurry of Blows, 7 to Stunning Strike each one), and again, can do this as long as they have ki to spend.

On the other hand, I'm allowing my monk to cast something like firestorm (which costs 8 ki, 7 ki on my second run) and they can only do this once (to count for the fact that high level spells like firestorm is an AOE normally only available to full casters). To me, this seems like a fair trade, and allows the monk to do one big epic thing, which is what Tier 4 should be about.

Summary

So, in short, the changes that the blog suggests are good, and this would certainly help the Way of the Four Elements monk to be less terrible as a subclass. I recommend you use the blog's suggestions (but of course I recommend the way I did it regarding cantrips, because I think my cantrip choices were better), but I feel that reducing the ki points by 2 (minimum of 1 ki point per discipline) is focusing too much on the wrong aspects, and I feel that reducing by 1 point is enough.

However, even with that, I feel like the Way of the Four Elements monk could do with a few more improvements, outlined in my above section, which will allow them to still "feel monkish" rather than feel like a subpar caster and help to bring them up to scratch with the other monk archetypes. Whether you want to use my extra features or not is up to you, but at the very least, the blog's suggestions are the minimum of what you should use to help improve this subclass.