He’s a superhero not because he got injected with some crazy superhuman serum, but because he has a willingness to self-sacrifice for the greater good. That’s why Stark’s argument (and Luke’s) is reductive and way too literal. Because everything that’s special about Steve isn’t physical at all.
In Captain America: The First Avenger, which was so godawful boring I don’t fault you for not having sat through it, Steve, still skinny and sickly, throws himself on a grenade to protect his fellow soldiers.
Of course, it’s a test to see who will do the morally right thing. And that’s Rogers. When you add his heroic morality to his super physical ability, you get a SUPER HERO. That’s really just math.
The serum just made it so the outside finally caught up to what was on the inside.