Why is it the concept of a solo king winning fundamentally objectionable?
Why stalemate ends in a draw

Because it's not winning. That's the joke here. You can't check a king with a king, let own MATE a king with a king lol.

I've done something like that before when I was the player with the lone king. But why shouldn't it be a win for black? White must move, white can't escape capture, white loses. In checkers a stalemate is considered a loss for the player who is in stalemate, but chess says that is a draw, go figure.

Because the point of chess is to KILL the enemy king, not TRAP, but KILL. In chess, u strike the man whose down until he's dead. You're seriously comparing checkers, a game where half the board isn't even used, to chess.

Since you dismiss checkers, in the chess variant played in China, Xiangqi, lacking any valid moves on your turn is a loss. The point there is obviously not to murder the king, as starving him to death seems satisfactory enough.
Chess is the way it is not because of any sort of deeper truth found within but because that's how it evolved. You argue that stalemate should end in a draw because the point of chess is to kill the king, but the point of chess is to kill the king because stalemate is a draw.
You keep arguing from incredulity and using circular reasoning, and it's not very compelling.

Since you dismiss checkers, in the chess variant played in China, Xiangqi, lacking any valid moves on your turn is a loss. The point there is obviously not to murder the king, as starving him to death seems satisfactory enough.
Chess is the way it is not because of any sort of deeper truth found within but because that's how it evolved. You argue that stalemate should end in a draw because the point of chess is to kill the king, but the point of chess is to kill the king because stalemate is a draw.
You keep arguing from incredulity and using circular reasoning, and it's not very compelling.
Checkmate!
Because if it ended in a loss for the stalemated player then in a King vs King + Pawn on the H/A file position, the sole king can win. It's already impossible to win with a pawn on H/A in an endgame, but it is also impossible to lose. No matter how bad the other player played, a solo King shouldn't be able to win.