What you are suggesting is the way blitz chess is played, just not real chess. It is one of the reasons I don't like to play blitz. If a person can't figure out how to force mate, they shouldn't win. The forcing totally against the opponent's will is what makes it chess. Not some childish gotcha. That's also why a draw by stalemate makes sense. Chess is a puzzle to figure out.
Chess doesn't end with the actual capture of the king. The rules would have to be changed so that the king must be actually captured. This changes checkmate from the end of the game to the signal that you might as well resign one move early.
Also, this would make the game a different game at the lower levels of play, since the highest rated players would almost never lose like that anyway. It would be a total patzer rule.
what do people think about the rule that you can't move your king into check? i personally think it's kind of strange since you're allowed to blunder all through the game and lose, but you can't blunder your king away? just curious as to what others think.
in my opinion, if you're dumb enough (drunk enough, tired enough, or whatever) to move your king into check, maybe you deserve to lose the game. what do you think?