The list of potential game types is enormous already without adding all the many permutations.
Think about just one example. Currently there is a 2v2v2v2v2, right? Ten players, 5 teams, one line in games played.
Now you could have:
2v2v2v2v1
2v2v2v1v1
2v2v1v1v1
2v1v1v1v1
So one line turns into 5 lines and that is just a simple case. Imagine how big it would expand to with 4-person teams?
4v4v4v3v2
4v4v3v3v3 and on and on and on.
Soron, the idea was suggested before and AFAIR Fizzer mentioned also technical difficulties in figuring out on which side you were, not only presentational ones.