I mean you can see the origins of the Fighter with a lot of classic pulp heroes, Conan (despite being called a Barbarian, is obviously a Fighter), John Carter, Lord Greystoke/Tarzan...really just about any Edgar Rice Burroughs protagonist, and even characters based on those archetypes, like Corwin of Amber.
These characters only occasionally use weapons other than swords (the occasional gun or raygun) or avail themselves of magic (or super science). They tend to be just as dangerous without weapons as with, and can readily use just about any oddball weapon they come across in a pinch...all of things which basically scream "Fighter".
But there are two key differences to note. One, these characters tend to have amazing ability scores, beyond standard arrays, point buy, or even the laws of probability.
And two, they generally have deep and varied skill sets acquired over many years- it's not uncommon for these archetypical characters to be long-lived compared to normal humans to justify this, but that's not a given.
This runs counter to the "zero to hero" fantasy at the core of D&D, where you're not playing Conan, not even Conan at level 1, but a slightly above average guy who will never quite reach the epic heights of such a character, as they gain attributes and skills at a much more conservative pace.
So in almost every version of the game it feels like you're not actually able to become the heroic figure the game tells you you're meant to be.
Look at some of the examples D&D occasionally gives you for who your character could be like, then look at that character, and look back at your PC, and realize that's not really true.
2e told us that our Fighters could be (among others) Hercules, Beowulf, Cuchulain, Hannibal, Alexander, Charlemagne, or Richard the Lionheart.
5e stops short of comparing you to iconic D&D characters (other than Bruenor Battlehammer in chapter 1), which is good; if someone came into the game expecting their Ranger to be Drizzt Do'Urden, I'd have to try and let them down easily.