Away from books at the moment, but... I'm pretty sure the Archmage has a defensive CR below 12 and an offensive CR above 12. Is cone of cold really his best offensive spell? If so, fine, cast it in the 9th, 8th, and 7th level slots. Confirm the AoE calculations on number of targets.
I'm pretty sure if you look at his best possible damage output by DMG guidelines, he is well above offensive CR 12.
Well it depends.
His 8th slot is tied to mindblank.
His 9th holds time stop. I don't know how that factors to damage.
But the archmages NPC relies on hitting 2 targets with each CoC and having them fail (or 4 successes) to reach CR 12 damage.
Okay, but my point was that you may have been misinterpreting the Archmage's expected damage output. I've got my books now, and for fun I just (over)analyzed the Archmage. I think I see the problem.
Your assumption is that the Cone of Cold hits only 2 targets. But why? In the example of an AoE attack, the DMG does suggest assuming it hit 2 targets... but that's for the young white dragon breath weapon, which is a 30 foot cone. Cone of cold is double that.
And sure enough, if you crunch the numbers on the adult white dragon, with a 60 foot cone breath weapon, it's offensive CR comes in well below the expected 13... if you assume it still only hits 2 people. Change that to just 3 people, and it nails it's expected damage output on the nose at 85.
And this still might be a lowball, since the adult white's HP are below expected (closer to CR 10), so arguably it's got a higher offensive CR than defensive. Maybe it assumes 4 targets, which would put it's offensive CR at 16, averaging the two out to the expected 13. Or perhaps it makes up the difference in legendary actions, which add a bit of gravy damage and resistances.
Back to the archmage, though... If we just assume 3 successful targets for each cone of cold, he doesn't even need to cast it into his teleport slot or anything. That dishes out a solid 108 damage, putting his offensive CR up to 17.
Follow that with an objective review of his defensive CR... it turns out, I don't think we even need to worry about time stop, except as a way for him to reliably start the fight with his buffs up. He's got 99 HP, but he has resistance to both spell damage and nonmagic weapons. I'm going to say this gives him an HP multiplier of 1.5 instead of the 1.25 normally given to a CR 12 monster with resistance, since the two actually dovetail extremely well. That puts his effective HP at 148, which is still a measly defensive CR of 6. But wait! His AC is 15, and the magic resistance also gives effective AC +2 according to the DMG. His effective AC 17 (compared to the CR 6 base of 15) means we increase his defensive CR by 1, to CR 7.
So. Offensive CR 17. Defensive CR 7. Those average out to... drumroll please... CR 12!
Looks right to me. You just need to play around with some of the assumptions being made about the monster. Not all AoEs can assume 2 targets when they all have wildly different areas. I would be pretty disappointed in myself if my BBEG could only tag 2 people in a massive AoE like cone of cold.
But it's not explicitly stated anywhere... the area of effect section for adjudicating TotM assumes PvE, with potentially large numbers of foes. They don't have an AoE adjudication table for monsters, which is a shame, because it means we have to rely on gut checks, common sense, and outright guesswork.
Anyway, hope that clears up where I was coming from. The Archmage fits in okay with the CR system after all, in my book.
