I'm not sure Hercules: The Legendary Journeys isn't a superhero show.Sure, but my point is that it will still feel like fantasy even if the thing doesn't have Tolkienisms and D&Disms in it. It will feel like playing through Greek mythology.
Supers can still work as a mechanical structure, and probably work well, but the "supers" fictional trope structures will be washed out. And if your supers ruleset has rules to actively support the trope structures, some of them will likely seem highly anacrhonistic.
I think you are making too much of the distinction. Gilgamesh and Heracles are the archetypes that became superheroes. The only real difference is the focus on nationalism versus altruism, but that certainly isn't universal as far as supers are concerned.