This is just a draft but the overall mission is to have a co-op implemented in the game first whether campaigns or other battles.
Co-op mode? How is what is suggested here much better than just playing human vs AI team games in the lobby. Those extra suggestion for special game modes can be implemented in the scenario editor. In fact I am sure there are some co-op scenarios in the mods browser. You are just asking for officially made ones.
I think the reason for success of co-op mode in Starcraft II is that team games feel pretty meh compared to its 1v1s. So playing 2v2 vs the AI wasn’t much fun. Also Blizzard put a lot of work and marketing into their co-op mode.
In comparison, in AOE2 team games are much better. The AI is much smarter. The devs would need to put an even bigger effort if they want to replace playing 2v2 vs the AI with a co-op mode.
Choosing the same color does this doesn’t it?