I like playing Wizards, and I like playing Fighters. Different animals, built for playing different styles.
I've quite enjoyed playing all sorts of characters over the years, but playing a 1e Magic-user or a 3e fighter are different mainly in a metagame sense, and which class is viable and has some depth or interest or potential on that front has shifted around a little over the editions.
But, I also find I'd like to pay quite different concepts at different times, too, and not necessarily have to radically adjust my play style or applied system mastery, let alone make substantial compromises to the concept, just to get something viable/playable that sorta fits.
5e is not exactly the nadir nor the high point of providing the tools to play the character concept (archetype) you want, without interference from the system, but the fighter is among it's less successful attempts, which is unfortunate, because it's the only option for many concepts.
It seems to me, for many players, the appeal of the Fighter is that the Fighter is nonmagical.
Like the appeal of Batman (nonmagical) versus Superman (magical). There is a kind of pride in being hands on and self-reliant.
That's part of it, but, I think, mostly indirect. The fighter is often the only class that fits many character concepts from genre. Heroes don't often cast spells in genre, and are very often warriors of some stripe. As you get to the edges of genre, blurring into action, sci-fi, and history, that only becomes more the case. You really have to get into comic book superheroes before you see the frequency of heroes wielding supernatural powers that you see with casting ability in D&D, and, even then, the sheer variety of such powers routinely used by D&D characters is quite rare (heck, even when you
do have a cb character wielding the bizzare breadth of power displayed by full casters, like a Dr. Strange or Reed Richards, it usually comes in the form of a author-force plot device, and mysteriously vanishes thereafter).
Batman and Fighters can be highly complex − including class build, features to choose for the specific situation, which equipment to use, and so on.
The build of a 3.x fighter could be, and a 4e fighter could be in play. The 5e fighter fails to live up to either. It's a DPR machine. The BM at best hints at what might have been had the class been given the same chance to shine as others.