The only drawback I could see would be people hiding in the last couple of minutes when they're in the lead, for fear of being killed and losing the match.
Of course, that makes it MORE fun for those NOT winning as they get to try to hunt down the leader and spoil their victory. You know, the more I think about this, the more I like it. It would prevent runaway games as well, where the kill limit is 20, the leader wins in 5 minutes and the others have only 2 or 3 kills, but the leader has died 10 times. Might balance the games better.
One thing I think should be removed, however, is the ability to kill yourself. I've chucked people to their doom or had a bead on them with a homing rocket and they kill themselves to deny me their death. That is the epitome of 'cheap'.