But my point is: What makes that player want to push the "auto win" button? There are lots of games with cheating, but also many more that dont suffer nearly as much from cheating, if at all.

Competitive games, especially ones that lean towards eSports and "real prizes" are going to have some incentive to cheat, but even in this genre there's games known for cheats and others that have better reputations. The question is what game design decisions can improve the urge of players to seek cheats in the first place.