There could be a rule that someone loses if they repeat a position!
Likewise there is no particular reason why stalemate could not be viewed as a loss for the player who cannot move - it is an arbitrary choice that it is a draw.
Overall, chess is simply an arbitrary game with a set of arbitrary rules. It doesn't matter much.
An interesting example from another game is the requirement to capture in draughts/checkers.
Anyway, I've long thought that if ever stalemate is abolished, the winning side should be the one that's forced to move into check.
Just remember that a lone king can stalemate a king and a-pawn/h-pawn, so a lone king would then be able to win on time against an opponent who still had an a-pawn and/or h-pawn.