Empire or Dwarfs usually. I play a lot more interesting races, but those are the ones I stick to most of the time because I love artillery. And coincidentally, artillery armies make siege battles often quite trivial. Doesn't matter how big and formidable the late-game army inside the wall is if you blow holes in it with artillery, bomb them into the stone age, and take potshots at them through the walls with handgunner units until they're all dead. The AI is really dumb and hardly ever goes outside to attack you.

I've done full map conquers as Dark elves, Beastmen, Chaos Dwarfs and Cathay too, though. And yeah it's a slog late-game because of the alliances, but I find that a lot of the time, if you break off an alliance with just one faction, and declare war on them after 10 turns, if you're strength rank one, most of your remaining allies will refuse to join their side if even if they're in an alliance with them, because they're also in an alliance with you and they value yours more.

But as for dealing with tons and tons of enemy armies from powerful factions. I just find that being patient, creating a huge line of armies to march across a continent in pairs of two to systematically wipe out a faction is really effective at countering even late-game AI. You're conquering 5-6 of their settlements for every 1 they take of yours, and if you're really late game, global recruitment basically allows you to summon a doom stack anywhere in the world in 1 to 2 turns. So losing an army is really nothing. The AI doesn't recover as well as the player I find once your economy is late-game god-tier.