Actually it would be better if they keep whatever fitness they are at - AND that injuries also stays on the player (magically disappearing injuries is just plain dumb!).
This does call for a change though - on the transferpage we gotta be able to see the fitness/injuries of the players we want to buy, then its up to the buying manager if i wants to buy a tired/injured player or not.

Removing any of them just cause programmers are lazy is the worst solution!