Since we can leave feedback once we have been eliminated from a game, I think it would also be helpful to be able to leave feedback about someone once they have been eliminated from a game.
As many have noted, games can go on for awhile. If someone gets knocked out early on, it would be beneficial to be able to leave that player feedback promptly, rather than waiting weeks or months to leave it once the entire game has ended. I am not suggesting that we be able to leave feedback for players still in the game, only those who have been eliminated.
This will improve the site by giving players who aren't strong enough yet to win games a chance to build up some feedback. Since some new players are assaulted with negative feedback before they have their sea legs, this could allow people to leave positive or constructive feedback in a timely fashion (yes, it could also allow more negative feedback as well). Since we remember bad things better than good things, it is likely that new recruits receive more negative feedback than positive particularly if they got eliminated early.