Well, I agree about the human part, but the fighter part? Not so much.
Aaragorn is totally a paladin. Or a ranger, depending on your view.
Did he cast spells? Heal with a touch? Have an animal companion? No. He was the inspiration for the ranger, but since then there've been skills added to cover what spells did so haphazardly for the early ranger, and the ranger has 'evolved' to use all sorts of actual spells much earlier. He might have been a 4e ranger or UA spell-less ranger, but not a PH ranger. Paladin is right out. In 5e, Outlander Fighter.
Gimli, Sam and Merry might be fighters, but Frodo and Sam are not. Bilbo is a rogue.
Bilbo was at least mistaken for a Rogue.
Conan the Barbarian. Its right in the name.
Howard's depictions of Conan didn't go in so heavily for the Rage thing, and certainly didn't invoke totems... Fighter or MC works at least as well. And, Barbarian, should have been a background like it was a kit in 2e. ;P
Robin Hood is totally a Ranger.
Doesn't cast spells, doesn't do anything D&D-identity-crisis-rangery, really.
Folk Hero Fighter, archery style, off you go.
Wu Xia stories default to the monk class.
Wu Xia use weapons, lots of them, often armor.
King Arthur is pretty much an iconic paladin as well.
Sure, always healing people by laying on hands and casting spells.
Lancelot had a 'fall from grace' that was paladin-appropriate enough. And Galahad, of course, is the prototypical paladin. They never cast spells, though.
Are self-referent.
Heracles is totally a barbarian.
He'd likely fly into a rage and snap you neck if you said that to his face. Y'know, in ancient Greek... ;P
Seriously, though, the one time he famously did 'Rage,' it was because Hera had driven him mad.
So, who are these legendary Fighter types?
Most of the characters you just mentioned. The rest of the Knights of the round table. Basically every other 'knight' that didn't run around casting spells and laying on hands. Roland and almost all of Charlemagne's Paladins, ironically (and one of them was vaguely a Warlock or something, too, weirdly enough). Beowulf. Hector. Pretty much the cast of GoT who aren't clearly rogues.
I mean, process of elimination: do you sneak around and stab people in the back? Do you go berserk? Do you have magical abilities? Three strikes and you're a fighter, there's nothing else left in 5e.