Deathmatch... last man standing gets bragging rights!
I don't think it would inspire team play, I think it would force people to stay back more. "If I stay on the UCB, they can't kill me". Medics would be a lot more popular though!
I think that a longer spawn time of 45 seconds or a minute would encourage more teamplay. 15 seconds, meh... I can wait. A minute? Man... that's a long time. Well, a long time given that in a minute a lot can happen in this game...