One less-aware idea that CoC brought to TRPG was that: Don't stat your "Invincible Beings"(tm).
"If you stat your Unkillable Great Evil, your players will try their best to beat that stat." Cthulhu itself was not that (relatively) hard to kill had already been a problem with earlier editions, but the final realization of the idea was d20Cthulhu that brought it to the general TRPG public.