I have thought about this concept, and correct me if I am wrong, but do you mean the seperate teams in 1 alliance have only 1 egg? *reads elaboration*
Yes you apparantly mean that, and the egg would be on one of the different island of the alliance. Now I think this is unfair, because the island with egg has to defend it. You say all the islands have to defend it to stay alive, that's true, but I doubt that will actually happen in game.
Now I also read this:
Alliance 3 (Gamma)(each island with a seperate egg): Light Blue (1 player) + Blue (1 player) + Dark Blue (1 player) + Purple (1 player) + Dark Purple (1 player) + Pink (1 player)
Now I would honestly LOVE to play this. You are still solo on your own island, with your egg, generators, defense, etc. but also still in an alliance. This is really what an alliance is, individuals bound together to find against the shared enemy.
You can still have your own tactics here (midcamp, defending, upgrading your generators, rushing, etc.), but you also gotta care about your alliance-mates.
From your elaboration I read that the alliances all have different setups in 1 game: 1 general egg, individual eggs, etc.
I think that's just too unfair, and no compensation would make this fair. 1 egg vs more eggs is just unfair for the 1 egg, because if that's gone they all can be eliminated. And that's only the first disadvantage, I could name a lot more.
There can very good be different setups for this, but in 1 game all alliances should have the same setup in my opinion.