It's more that you increase the chance of detonation with a higher charge temp (so you have to reduce power to avoid it going pop) plus a cooler charge is denser so while you might be right from a strict thermodynamics POV its not that simple in the really real world.
IIRC Rotaries really dislike detonation too, even more so than piston engines.

IIRC Rotaries really dislike detonation too, even more so than piston engines.