Same deal with Iron Man, really, though arguably Kirk can do more thanks to future tech. He can certainly travel faster and packs more firepower. He beat death. He's grappled with opponents considerably stronger than him and won. And as was mentioned earlier, he repeatedly saves the planet. He has a suit that readily makes him identifiable as his character.
The thing is, the tropes that we associate with comic heroes apply to both Shatner and Pine Kirks. And why do they have those tropes? Because they tell stories about heroism and optimism with abilities far beyond what we have today (however those abilities are quantified) in order to provide escapist -- but idealistic -- fantasy.
Even if we want to narrow down the route, we'd have to consider that there are spacefaring heroes like Adam Strange and Starlord who are cut from the same fabric of pulp heroes, just like Jim Kirk. Dashing, charming, charismatic, sometimes pragmatic, but ultimately a fearless, peacekeeping explorer. Someone whom the audience strives to be.