This isn't very interesting, but I used to believe that the rules about checkmate didn't really change the nature of chess. Some of the forbidden moves - moving into check, or failing to move out if possible - are always a mistake, so if you just played until someone captured the king, the game would only be different in cases where someone made an obvious mistake.

But if you can't move, the game ends in stalemate. So forbidding you to move into check means that some games end in draws, where capture-the-king would have a victor.

(This is still armchair theorising on my part.)