The only way to win, aside by flagging or resignation, is by checkmating you’re opponent. When you stalemate, you cannot checkmate, it’s as simple as that.
As a metaphor, consider you have a huge army outside a castle. The king is trapped inside, but you can’t get to him. You can shake your swords all you want, and he can’t move, but you just can’t kill him. You can’t lose, but you can’t win.
The stalemate rule makes you a better player by forcing you to be more precise with checkmate and not just sloppily throwing pieces around your opponent’s king. It also offers hope to the losing player in the final moments that a position can be saved.
You play a close game where it's pawn + king vs. solo king. You do all the right moves up until the very last one and get your queen. Boom, stalemate. It's pretty easy to force. The opponent can't move. Why is that your problem? Stalemate should be abolished. Period.