At the same time, maybe these 'negative' cheats would function better as difficulties that may be accessible through a select difficulty setting in the menu! And then the solution is to make all cheats feel beneficial to the player!
That sounds like a great solution, yeah! :) The points you bring up are good, and it's a totally valid interpretation of the theme; but as you say, when I, personally, hear the words "the player must cheat" I tend to assume that cheating will benefit me.