I have never seen any posts that even mention reaching the 'team' level of alliance. As far as I can tell, no one uses it. What I would propose is a set bonus that each civ gives to each of their 'team members' automatically. (i.e. 5-10% diplomacy bonus for teaming up with the Humans etc.) This would actually give players a reason to team up.
I would also like to see this extended to minor races (maybe with a smaller bonus) which would give players a reason to treat them as more than a speed bump.
Scincerely,
Scintor