Justice and Rule
Legend
Ok. A fighter trains for hours a day until they are peak fitness. Maybe even slightly better. What is that worth? He might be able to jump father, but are we jumping miles? We might lift large boulders, but are we toppling mountains? We might kick down a steel door, but are we flipping the Tomb of Horrors upside down?
Again, if the origins fit the powerset, I'm ok. But I keep getting "Taran was a level 1 pig farmer, but 15 levels of adventures later, he wins staring contests with the Sun".
Okay maybe it's just too obscure a reference here, but it felt appropriate. But really, @Neonchameleon nails it: we need to use the same frames of reference. You can't talk about "real world training" because there's no comparison to "real world magic". You brought up Boromir, but why are we not basing what casters can do on Gandalf? That's the problem here: people want to pick different kinds of fiction for different classes. For whatever reason, fighters aren't Hercules or Gilgamesh but mundane people, while casters are judged against... well, D&D casters, because the game archetype is uniquely powerful compared to most depictions of mages.
I think @Stalker0 gets to all you need: a passing explanation that there is something special that can be brought out in everyone through training. Martial spirit, the hardening of skill and steel... however you put it, it can be there. I always tell my players that everyone channels the fantastic in their own way: Wizards mold it through "magic", Barbarians unleash it through rage, Monks channel it through Ki, and Fighters harden it through training. Like One Punch Man above, you can eventually reach ridiculous heights merely by training. At a certain point you just begin to cross over, see what you couldn't see before, cut what you thought uncuttable, start to see things in a way that you can navigate the steps to do the impossible.