Wikipedia says
A superhero or superheroine is a stock character that typically possesses superpowers, abilities beyond those of ordinary people, and fits the role of the hero, typically using their powers to help the world become a better place, or dedicating themselves to protecting the public and fighting crime.
So yes, he is definitely dedicated to protecting the public, but it feels wrong to call him a super hero. What do you think?
I feel like superheroes have a plot constancy that forces them to stay superheroes. Their superpowers may lapse, but they generally get them back and feel justified in using them. Their main villains may fall or seemingly reform in one episode or series, but usually return as bad as ever. In Legends, Luke’s fight with the Empire is almost over before it has begun. Cleaning up the Remnant and warlords falls to regular X-wing pilots and commandos in the New Republic era. Luke is more of a mediator than a fighter and mostly withdraws from heavy use of the Force by the New Jedi Order era. Even the new enemies of that era don’t stay enemies forever. Instead of forcing constancy, Legends allows conflicts in these eras to be “solved” and to permanently change characters.