I think it is impossible to balance. Some civs quite simply do better in team games, particularly if it’s a closed map. Prime example, Britons, they are quite annoying to deal with in very closed maps, especially if they have adequate support. However, the Britons aren’t great in open maps, they can’t take advantage of chokepoints with mass Longbowmen.
1v1 Arabia is basically where I think the game is balanced around. Where games can end in less than 20 minutes or even less and end in the feudal age. Many late game boomer civs won’t get these super awesome units.
If chess can’t be a 100% balanced game despite both sides having the same pieces, you can be 100% sure that AoE2 will never be fully balanced, considering how different the civilizations are.
Despite this, the civilizations are reasonably balanced, and their impact on the outcome is not greater than the players’ skill levels.
Besides, perfect balance would just make the game boring.