Is this Generalist Wizard balanced compared to the official wizard subclasses?
The intent is to make a wizard that, instead of focusing on any particular school or application, just gains more knowledge of and control over magic, the wizard equivalent of the Champion or Open Hand subclasses.
Arcane Expert:
At 2nd level, you gain proficiency in Arcana if you are not already proficient. You add double your proficiency bonus when you make an Arcana check.
Rogues and Bards can get expertise in Arcana, so it's probably balanced for Wizards to do the same.
Expanded Memory:
You have studied magic so much your mental capacity to remember spells has increased. Also at 2nd level, when you prepare spells, you can prepare an additional number of spells from your spellbook equal to your proficiency bonus.
A wizard gets at least 44 spells by level 20, and usually much more from copying. They can normally prepare 25/44+, and this raises it to 31/44+, so this is at most a 24% improvement.
Ritual Master:
At 6th level, you gain the ability to record any spell with the Ritual tag into your spellbook, regardless of if it appears on the wizard spell list or not. You can cast any spell with the ritual tag as a ritual if that spell is recorded in your spellbook and you have your spellbook on you. Whenever you gain a level in this class, your 2 free learned spells can still NOT be ritual spells not on the wizard list.
Note that this does not give any ritual spells immediately, and they must be found during the wizard's adventures and gameplay, giving them a gradual increase in mostly very situational utility spells.
Cantrip Mastery:
At 10th level, the easiest spells become even easier for you. As an bonus action, you can choose one cantrip from any spell list. You learn that cantrip and can cast it using your Intelligence modifier until you use this bonus action again. You can use this ability twice, and you regain all uses when you finish a long rest.
This is very similar to the 10th level cantrip for the job UA Artificer feature, at this level the wizard has 5 cantrips anyway, so this just adds utility, but is very flexible.
Archmage:
Through tireless study, you have trained to control the Weave to the point you can sometimes control, through great effort, two spells at once. At 14th level, if you are concentrating on a spell, you can now cast a second spell that also requires concentration. If you do so, you immediately suffer a number of levels of exhaustion equal to the sum of the spells' levels. Levels of exhaustion gained in this way can only be removed via long rests. If you fail a check to maintain concentration, both spells end. You cannot use this feature if you are somehow immune to exhaustion. You cannot concentrate on a third spell.
Being able to concentrate on multiple spells is extremely powerful, and is supposed to make up for this subclasses lack of combat helpful features the other subclass' have. However, I believe it is balanced because rest-only-curable exhaustion is a very high price to pay, and since 6 levels of exhaustion is death, only 5 total spell levels can be concentrated on at once. This does allow free concentration on 2 cantrips at once, however there are only 6 cantrips that require concentration, only one of which (create bonfire) does damage, and one of which is the worst cantrip in the game, True Strike.
Best Answer
Overall / TLDR
The lv2 features are quite good, top tier abilities, but a bit of attention and fiddling with the numbers can keep it from being overpowered. After that, however, nothing really stands out as powerful. Both the lv6 and lv10 features have only marginal utility and the lv14 one is just not worth it for the drawback as it is now. I would recommend limiting Expanded Memory to +2 and adding new features or expanding the existing ones on lv6/10. Rethink the capstone. Hard.
Arcane Expert
This is basically half a feat (Skill Expert or Prodigy). Not really game-breaking, but it seems to replace the half-cost scribing feature of the basic subclasses, and will be more powerful than those in most cases.
Expanded Memory
All subclasses start with a fairly useful feature, and I think this is about on par with the better ones (Sculpt Spells and Portent). It will still be more useful on lower levels, where the limit is more restricting. My wizard buddy in a campaign that went over lv20 usually couldn't decide what to prepare in his last 4-5 places towards the end and we rarely encountered a problem with him not having prepared something. You should playtest the actual number of spells granted anyway.
Ritual Master
The similar feature for the warlock is strong because they get access to wizard rituals. Wizards already get access to most ritual spells, so this is pretty lackluster for them.
Cantrip Mastery
As others have also pointed it out, the main candidates for this will be guidance and eldritch blast. The former is usually available to any party with a cleric or druid already and won't break anything anyway. And without the buffs warlocks can stack on it, the latter is mostly useful since it deals force damage. Spare the dying or shillelagh might be used in desperate situations. Overall more utility than power, but not a lot of that either.
Archmage
The exhaustion limitation is too punishing. Even getting two lv2 spells going would get you lv4 exhaustion. At lv14 those are throwaway spell slots usually, mostly used for shield, absorb elements or misty step in my experience. They are just not on par with the problems you are supposed to solve. I do not expect that combining two of those would be so much of a game-changer that you would cripple yourself for 2+ days to do it. As written, this is practically unusable.
What I would recommend is to limit the level of spells that are eligible to lv5 (like Overchannel), but add only 1 level of exhaustion per use. (I would also consider giving one "free" use per long rest.) Also, do not forbid magical means of healing it. If someone has a spare lv5 spell slot and 100gp in components for a greater restoration, let them use it. This is in line with the utility over power "feel" of the subclass: instead of shapechange, you can use greater invisibility and telekinesis at the same time (for example).