As Totero notes, changing stalemate in this fashion would drastically change endgame play. Currently, one must learn how to recognize different King/Pawn endings, and how other pieces interact with these endings. Opposite- vs same-square Bishops, Knight/Pawn vs Knight, Rook/Pawn vs Rook, and other basic variations.
Changing stalemate to a win would throw much of that out the window. Who cares whether White or Black has the opposition? Just run that Pawn down the board. Rook/Pawn vs Rook? No worries, just force a trade, and the win is guaranteed. It might not be fair to say that this would trivialize endgame play in reducing it to mindless exchanges from material superiority, but it would be a drastic change.
Put another way, it takes more skill to calculate and remember ending positions than it does to march one's way to a stalemate, and the stalemate rule is intended to recognize that fact.