Missing the point. The point is, that while taking fighter levels is certainly common, I've yet to see a single classed fighter. Fighter is the dip class.
I have. Via the simple expedient of not using multi-classing. ;P
But, it's not what I've seen taken as part of the personality of the character. All that stuff - personality, background, all the actual role playing stuff - comes from the other class.
Background literally comes from "Background," with which personality traits are also associated. Mechanical support for the character's abilities - most of the player's practical agency - comes from class.
So, we see RANGER/fighters, PALADIN/fighters or whatever.
Mearls has lamented making the fighter so 'generic' (But, really, to avoid that he'd've had to have had more magic-optional classes, maybe even a genuinely non-magical class.)
The problem is that the Fighter doesn't get anything that wows so it appears to be weaker ...
Action Surge + Extra Attack = 'Wow.'
The fighter also has second-best HD, good armor & weapons, and can literally be the strongest (STR primary) PC in the party - it doesn't appear 'weak,' it's just profoundly lacking in versatility and interest, and on close analysis, has no particular advantage in sheer combat power.
I would say the 5th edition fighter is probably better and more fun than either AD&D or d20!
Considering the 3.x/PF fighter was Tier 5 and the AD&D fighter was feature-impoverished, that's an incredibly low bar. ;P Even then, I think 'better or more fun' would be fairer - the 3.x fighter may have been deeply inferior, and the 5e fighter less inferior, but the cusomizeability and elegance of the 3.x fighter could be a lot of fun to work with, and even, when executed exceptionally well, to play.
And since 5e offers better options to fleshing out your Fighter concept (backgrounds, multiclassing, not to mention three subclasses built-in)
Better than 1e AD&D, or Basic, anyway. Every edition had MCing, only in 5e is it DM opt-in, only. 2e offered Kits, BECMI reputedly had all sorts of stuff I'm not familiar with, 3e had far more bonus feats, and 4e had backgrounds, two variations on MCing, three sub-classes - even more if you consider 'builds' of the retconned 'weaponmaster' sub-class, and hundreds of powers, just for the fighter, plus two more comparably-developed and option-rich non-caster classes that the 5e fighter vainly tries to cover.
What? You're saying repeating the design of the 3.5 Fighter with only minor adjustments didn't make much of a difference!?
The 5e fighter bears virtually no resemblance to the 3.x fighter, which was a uniquely elegant design - even if it did have the misfortune of being dropped in Tier 5.
Unless you're willing to have a Wuxia Fighter, you're never going to get the Fighter on par with other damage-dealing classes.
The game could always go there and let DMs who wanted a strictly inferior fighter shave off the features they don't want.