It's incredible how so many DMs are ignoring the concept of setting up your own enemies. You don't have to use this exact stat block, that is one of the beautiful things about DMing, you're allowed to make an archmage with spell slots that has a list of spells. If you are an experienced enough DM to run a spellcaster with numerous spells and spell slots, you are also experienced enough to homebrew a little and give the archmage spells you want. However, this stat block is good for a DM that wants to just have a spellcaster that they don't have to keep track of as many things for.

Rules as Written, I don't see why not. Rules as Intended, its still classed spellcasting so it might be best to use spellcasting rules despite the lack of spell slots. On the other hand, I believe they did this to be simpler for DMs that don't know how to run spellcasters yet, so it might not be expected of them to know that rule, so maybe RAI is actually that they can?

I guess with RAW being clear and RAI not being clear, you should go with RAW. Though, I don't think it matters all too much, since the person using this statblock is the DM, and they can override and follow rules and a whim if they so wish. They can decide if they want it to work that why or not whether it is RAW or RAI.

I mean, thats kinda what many Wizards are in D&D. Fighting Guards, Commoners, Goblins, Kobolds, any low powered but common infantry would get blasted by fireball or other AOE spells. One Wizard with one Fireball can kill several of these guys in one turn, so spellcasters are uniquely great at taking down small armies, espacilly when they have more spell slots like an archmage would. Not saying I disagree, with it make sense spells wise.

Arcane burst wise, I have no idea how they can arcane burst so often thought. Spells take a while to cast over a sword swing, and even if this is meant to be the "basic magic blast" of many fantasy stories (which in that case why hasn't such an idea been introduced sooner outside of the warlock only Eldritch blast for all classes as a cantrip), why is it so powerful. They are essentially blasting what would essentially be a cantrip based on the very idea of it four times per round, each one doing as much damage as a 17th level Warlock's Eldritch blast. I know you cast 4 Eldritch blasts at that level, but each one does 1d10. You essentially have an Eldritch blasts worth of Eldritch blast (16d10, or 988 average damage, which is more than the 9th level cone of cold assuming you hit two people in hit and one fails their roll [12d8=54] and one succeeds [6d8=27] [54+27=81]).

The damage is so high that it does make me wonder why you would bother casting many of the other more limited spells, especially those who's AOE capability is more sitautional like the line of Lightning Bolt. It feels too strong both damage wise for what it supposed to be and fun wise because why cast the other spells on the list unless you are at an amazing opportunity where you have nearly all players within cone distance and can thus guarantee some damage with an average higher than 4 arcane burst all hitting (if 4 people succeed, it does an average of 4x6d8=108 damage, more if someone fails).

Quote from ITakeNoBigL5 >>

I mean, thats kinda what many Wizards are in D&D. Fighting Guards, Commoners, Goblins, Kobolds, any low powered but common infantry would get blasted by fireball or other AOE spells. One Wizard with one Fireball can kill several of these guys in one turn, so spellcasters are uniquely great at taking down small armies, espacilly when they have more spell slots like an archmage would. Not saying I disagree, with it make sense spells wise.

Arcane burst wise, I have no idea how they can arcane burst so often thought. Spells take a while to cast over a sword swing, and even if this is meant to be the "basic magic blast" of many fantasy stories (which in that case why hasn't such an idea been introduced sooner outside of the warlock only Eldritch blast for all classes as a cantrip), why is it so powerful. They are essentially blasting what would essentially be a cantrip based on the very idea of it four times per round, each one doing as much damage as a 17th level Warlock's Eldritch blast. I know you cast 4 Eldritch blasts at that level, but each one does 1d10. You essentially have an Eldritch blasts worth of Eldritch blast (16d10, or 988 average damage, which is more than the 9th level cone of cold assuming you hit two people in hit and one fails their roll [12d8=54] and one succeeds [6d8=27] [54+27=81]).

The damage is so high that it does make me wonder why you would bother casting many of the other more limited spells, especially those who's AOE capability is more sitautional like the line of Lightning Bolt. It feels too strong both damage wise for what it supposed to be and fun wise because why cast the other spells on the list unless you are at an amazing opportunity where you have nearly all players within cone distance and can thus guarantee some damage with an average higher than 4 arcane burst all hitting (if 4 people succeed, it does an average of 4x6d8=108 damage, more if someone fails).

 So for cone of cold it is 12d8 since its 9th level for some odd reason, so if you catch at least 3 people, it will out damage spamming the base arcane burst, but only if you can catch at least 3 people and that's assuming they fail the save and don't have any cold resistance, if they succeed you would have to catch 6 players which is way bigger than most parties, and lightning bolt is literally never going to be used at all unless you the DM are intentionally throwing the fight. For arcane burst I honestly wonder if they made a mistake having it be 4 attacks instead of 3, since all the other spell casters only get 3 even the CR21 Lich. 3 would bring the Archmage damage more in line with CR12 higher tiers.

Honestly the most terrifying thing is that if the Archmage just casts fly, now you have a flying artillery battery that will 100% one turn any player he focuses on at appropriate level, and with an effective AC of 22 not much is likely to hit him at a range of 150 feet. That puts him out of range of cantrips except the warlock invocation boosted eldritch blasted and out of range of almost all spells since they have a range of 120 ft at most usually aside from fireball and lightning bolt. In a fight with a level 12 party, this guy can just obliterate 1 character per turn, maybe 2 if one of them is a squishy wizard and gets high rolled. In addition to that the Archmage has an effective AC of 22, making it one of the highest in the monster manual and the highest AC CR12, because most fights last 3-4 rounds and he gets 3 casts of shield, since I cannot imagine ever using counter spell over shield especially with permanent advantage on spell saves anyways. It has average hit points, but one of the highest damage per turn in the entire monster manual, out damaging most CR20+ if you don't count legendary actions. There is literally no combat reason to ever casts ANY SPELL with this monster, arcane burst will out damage almost every spell in the game against an average party size, and because it is an attack roll it is way more likely to actually do damage. Playing intelligently, and consider this guy's INT you should play them smart, you would focus all attacks on 1 player till they are done, since spreading out damage is foolish since a player at 1 HP does the same damage as someone at max HP, so even in that rare instance where an AOE spell might out damage the base attack, it's still probably a bad play since it might not down the players it hits.

The people saying you can just homebrew a little to give the archmage whatever spell you want seem to be missing the fact that there is no spell in the game that is combat oriented (so no Wish, Simalacrum, clone, etc...) that would be better than just spamming arcane burst. The only exception is meteor swarm, but funny enough that might not actually be useful since it will probably catch the Archmage in the radius as well and being a dex save is likely to be passed by the players, meaning even METEOR SWARM might not out damage just spamming arcane burst. Even worse since Fire resistance is common, and barbarians will half the damage regardless while rogues will probably just not take any damage at all with evasion. The only spells I could actually imagine using would make this guy become a solid CR22+ with things like Foresight for permanent advantage and all enemy attacks have disadvantage, which would frankly make this guy more challenging than anything in the MM that I can think of, Tasha's Otherworldly Guise to make it effectively 24 AC with even better flight and several immunities, or Greater invis to act the same as Foresight but would require concentration and mean you cannot use Fly. This guy's base attack is literally better than every damage dealing spell outside of extremely specific AOE instances using 9th level spell slots, using Force damage which is almost impossible to resist and at the longest range in the game that doesn't come with disadvantage, all while having an effective AC higher than 90% of the monster manual and permanent spell save advantage while fighting characters meant to be only at level 10-12 supposedly. Anyone whose complaint is just that they need more spells to be better is insane, they need more spells so that they don't just TPK by spamming their basic attack.

I miss when spellcasters had levels in classes.

Quote from darknessfighter >>

I miss when spellcasters had levels in classes.

Why? Of all the things they got rid of this is something I am not just okay with but honestly I can appreciate it being gone to save a little bit of space. Having the class levels is completely pointless if you know what their maximum spell level is, which we clearly do as the Archmage can cast 9th level. It has the Wizard sub tag, and it can cast 9th level spell slots, so by default they have access to what more do you need to run the encounter? The wizard Subclasses have all features by level 14, so if you really want to add subclass stuff just knowing they can cast 9th level gives you all the information you would need. If you somehow need hyper specific levels, then quite frankly just homebrew from the ground up using player character rules at that point and paste on Arcane burst. These are meant to be one and done enemies, not long term characters or NPCs, things like exact class level is just wasted space on the stat block.

Initiative should be +6 not +7

Also in Regards to AC, old Archamage has AC 12 (15 with Mage Armor)
Since this is a nasty burst dpser either revert to Old Ac or simply run it as AC 17 (Dex + Int)

Mage Armor is just for show or to cast on someone else.