Should Fighter as a class exist?

I'll preface this by saying I'm not really keeping my ear to the community, and though I've played in a few campaigns I'm nowhere near the most knowledgeable in the game or lore. So, apologies in advance if this is an argument that's been done to death or something.

That being said, what's the purpose of Fighter being a class? It doesn't have much of an identity beyond "guy who fights". The sorts of archetype that would normally be left as part of the character get completely left for (to be clear, pretty cool) subclasses, which just seems, lopsided? No other class has ALL of their subclasses so important to giving an identity to a character.

To the designer's credit, it's clear that there's a lot of freedom given to what a Fighter can be, which seems to be the intention. But that same freedom leaves the rest of the class nothing much to do or be, especially at higher levels. I completely get the idea for there to be a more general martial-focused class, meant to encompass general soldiers and knights and whatnot, but comparatively it generalized way too hard in my opinion.

Mechanically, it also seems to eat a lot of potential for other classes due to balances around overlap, particularly around Ranger and Monk. While Fighter is considered a generally better class, it can't fit niches another class would do better. From what I understand Barbarian does better damage per turn, and Paladin gives better support.

I just can't help but wonder if it'd be better if it's skills and abilities were put into other classes, if it'd be healthier. Or at least, some sort of warrior class with some better focus on what it wanted to be.

Or I could be missing something? Let me know. (Though, I think Fighter should at LEAST get a better name.)