Lovecraftian Superheroes or the Doom That Came to Comics!
Lovecraft plus superheroes? Interesting combination. Superheroes are notorious for violating any and all physical laws, of course. So… what if there's a reason supertypes can break the laws of physics?
What if the ultimate power source of any superhuman ability is some sort of Eldritch Entity From An Uncomfortably Far Realm?
Given this premise, supertypes must therefore be in direct, intimate contact with Cthulhoid influences every time they use their powers—complete with the sanity-breaking side-effects of said influences. Not everyone will be able to withstand those malign influences equally well; the ones whose minds break under the strain, will make up a disproportionately large fraction of the supervillain community.
Go ahead, write up a preposterously overpowered hero for your character. That character's excessive power level will be accompanied by an equally excessive degree of Cthulhoid… call it 'taint', perhaps? …in their life.
As for the Lovecraftian entity (-ies) which are the source of superhuman power, they probably shouldn't have any awareness of the effect they're having on mundane Earth. After all, one hallmark of Lovecraftian horror is the notion of vastly powerful Entities which are, not truly malevolent, but instead, supremely indifferent towards humans. They don't wish us ill; they don't wish us well; they don't even notice us.
The continuing subtle influence of Lovecraftian entities would go a long way towards explaining why characters in superhero universes tend not to behave the way normal (sane) people would…