well there are benefits to the stats and of course the obvious downsides as mentioned.

Benefits: increased competition! Brings people back to the server to beat their high score and others, adds another element to the game.

Downsides: encourages 'stat' whores. More engineers, snipers etc who are trying to avoid deaths as much as possible. Less teamwork as people less inclined to take risks and rush/suicide for objectives etc.

Although with the new update that's pretty irrelevant as everyones rushing/suiciding to stat up their pyros. (then again with the new plugin limiting the servers to 2 pyros per team, that point is also defunct)