The thing your build is most obviously missing is a bread-and-butter spell - something low-level that is usable with both Heart of the Storm and War Caster. You've ruled out thunderwave and shatter due to the noise, and while you didn't mention witch bolt I assume you've ruled it out on account of it being crap.

What you need is chromatic orb. It's 1st-level, on the sorcerer spell list, can deal lightning or thunder damage (handy for resistances or immunities), and works with War Caster.

After that, everything else is fairly minor. Since you only get 1/3 of the benefits of Sentinel, I'd recommend a different feat. Elemental Adept is a possibility, but if you're planning to be in melee, Crossbow Expert would prevent disadvantage on your eldritch blast and chromatic orb.

I'll try to answer your concerns one at a time, then give you my experience with a similar issue.

1. Yep... Eldritch Blast is extremely potent and has almost no downsides. It's primary purpose is to give the Warlock a best-of-breed damage cantrip, and it does that very well. Your assessment is spot on. I think the only thing you might be glossing over is the fact that to get your damage expression, you'll need to hit 8 attacks in a row. Assuming you're min-maxed, your plus to hit will be +11, whereas the average AC you'll be facing is in the low 20s. Although your max damage expression is 8d10+8d6+40 damage, your statistical average is probably closer to 4d10+4d6+20. Still very potent, but not quite as astronomical.

2. In terms of pure damage, you are correct that this is probably more optimal than Disintegrate (although again, you'll need to take the statistics of attacking vs AC versus making a Dex save against).

3. This is a standard Sorcerer ability that allows the Sorcerers to cast more spells. In a DMG Approved, 8-encounters-per-rest adventure this is necessary to keep them competitive. In a real-life, 2-or-3-encounters-per-rest adventure, this makes them very powerful. If you followed the DMG to the letter then your Sorcerer will likely have to ration out this Eldritch Blast hailstorm, which would bring the power level down a bit.

4. Yes, your strategy is superior to Haste insofar as dealing damage. You don't gain the additional speed but at level 20 speed is meaningless anyway. However, Haste also gives you a +2 to AC and advantage on Dex saving throws, so the true winner depends on what encounter you're facing at that time.

Now, in my experience, this is what I've seen.

Level 20 spellcasters are absolutely insanely powerful

Any spellcaster that makes it to level 20 is essentially a demigod. Comparisons between abilities at that level is very difficult, because they're all so absurdly capable.

In this case, your Sorcerer is extremely good at dealing force damage to one creature at a time for about 9 turns per day (more if you sacrifice your spell slots). However, at this level the other casters in your party can summon things like Tsunami, Meteor Swarm, and Storm of Vengeance that, due to their AOE attacks and the fact that level 20 encounters are usually brimming with minion-type characters, can do far more damage in a single round than your Sorcerer can output all day. There are also status-effect spells like Imprisonment, True Polymorph and Wish that can completely end an encounter before it even begins. So while your Sorcerer is good at damage, they by no means outclass other casters in the ability to end encounters quickly.

This leads me to my second observation, which is

Martial characters at level 20 are complete jokes compared to spellcasters, and you can't even begin to compare them to spellcasters

In your examples you're comparing your Sorcerer to a Fighter for additional damage gained by Haste. A level 20 Fighter is so far behind a level 20 Sorcerer that it isn't even funny. By level 20, the Fighter is completely outclassed in all areas of combat. It really isn't even close. By level 20, the Fighter's only job is to stand around and try not to die while the casters finish the encounter. If you try to find parity between casters and martial characters (especially at high levels), you're just asking for disappointment.

Finally, to answer your question directly, in my experience (for something similar but not exactly the same, basically house-ruling away certain spellcasting abilities at high-level play):

If you house rule this away, your Sorcerer will probably be mildly upset at you for a few games and then forget about it

It sounds glib, but really this houserule won't affect much other than the Sorcerer's damage output per round. In our case, the affected player was upset at first, but quickly realized they were still incredibly potent in combat. They never quite achieved the level of power they envisioned, but they didn't take long to adapt to the new restrictions.

The reason I don't believe that this will be a big deal in your game is that there is nothing mechanically that this build gives you other than massive amounts of damage. Anything the party could do with this build they can do without it. Mechanically your end-game encounters will take longer (your Sorcerer is now doing about 50% of the theoretical damage they would have before), but at level 20 the combat encounters are extremely variable and swingy. There are simply too many encounter-ending abilities on both sides that it probably won't matter much.

As long as your Sorcerer hasn't spent the last 20 levels crafting this character to have this ability and you're taking it away at the last minute (which would be pretty mean), then aside from hurt feelings there's going to be almost no difference (at least in my experience).