Y'know, 5e was meant to be an edition that would work for more play styles than prior eds had. It turns out, mathematically, that it 'works' in so far as comparative DPR goes (which is, like, combat, so not necessarily more broadly) for a tightly proscribed range of pacing. That's a bad thing for the self-proclaimed 'big tent' edition, as styles that use any other pacing are going to experience imbalances.
Does it work for some styles of play that naturally fall into or outright force that pacing? Well, as far as DPR goes, it should. And, some folks have reported that, for them, it does.
OK.
From my perspective, a 30% different in damage output isn't that large.
Especially if the damage looks different.
Two characters, one doing 30% more damage than the other, are peers.
So, the damage model that "doesn't work" -- where we have a 5 minute adventuring day, and the wizard does 30% more damage than the fighter -- the two characters are peers in combat.
As peers in combat, itemization (magic items, which is explicitly a DM tool in 5e), optimization (the degree to which a player tweaks their character), luck (literally how the dice land) and situation (the tactical details) can easily trump the difference.
And sure, out of combat the wizard's (or other spellcaster) trump card abilities is pretty large. But it is also not completely insane; as an example, a single uncommon magic item (winged boots) can make a L 5 fighter have as much or more magical utility than a typical L 5 wizard.
Sure, you can throw those boots on the wizard as well: but the point is that their difference can't be that huge when a single modest item bridges the gap.
And the two types of character are going to appeal to very different players.
And yes, this does mean there would have been piles of room to increase fighter utility and 5 minute day power output. But imperfection is not unplayable!
Note that I've said nothing about DM fiat - I'm just looking at the variation between character types, and seeing how large it is compared to other game elements.
This does mean that an optimizer who wants to optimize maximally may end up playing a wizard and not a fighter, exaggerating the imbalance; however I'd argue this only really matters at the highest end of optimization, when you start doing mass buffed minionmancy, nuclear wizards, or the like, because an optimizer maxing out a non-spellcaster can still get pretty far.
I can attest to this, I saw many people play Fighters in 3e (or at least dip Fighter) because of "all the Feats!"- despite the fact that most of the Feats were garbage until you met strict prerequisites. Heck, I played several myself, since I would often find some niche Feat that I really wanted to build around, lol, especially in Complete Adventurer and the PHB2.
I did always want to try a Tome of Battle class, but I never got the chance before nobody wanted to play 3.5 anymore in my area.
Heck, I even played a Fighter in PF1e for much the same reason, those crazy combat Feats, lol.
And as for AD&D, sure, Fighter was a strong character choice, you had great survivability, and while there were better classes for doing what Fighter did, they usually had crazy ability score prerequisites or roleplay restrictions that kept Fighter from being truly overshadowed.
I saw a lot of people trying out Fighter in 4e, without realizing it wasn't actually the "beat up people with big weapons" class...and some kept trying to optimize their melee damage even when they did figure it out, even when the Barbarian was available (heck, I saw a few people play Warlords with the same mindset!).
The class fantasy remains strong, even though I don't really believe there's a lot about the class that's special in 5e. At this point, I don't have any real desire to play another Fighter (at least, not a single-classed one), but maybe if a really neat subclass is printed I might change my mind.
Oh, 4e Fighter ended up as a pretty good beat them up class.
Its feat support grew and grew. As a PHB1 class and a popular one it got more feats than any other martial. And some of those feats where better than average; when you cherry picked the best ones, it got insane.
High-optimization in 4e generally involves spreading your menu of options as wide as possible then picking the best from them. This was made worse by the tendency for 4e designers to see a power gap and patch it with a feat (like the avenger "add attribute to damage" paragon tier feat) that you could poach.
Sometimes this meant you leaned hybrid. Like, a hybrid ranger-fighter two hand axe build that grabbed per-tap abilities from fighter (the per-encounter +2 damage/-2 AC stance). It took off-hand and interrupt attacks from both; but the majority of its feats where fighter ones. The main thing it got from ranger was a single at-will power: twin strike.
---
A problem I have with the 5e fighter is that until level 11, its only strong "thing" is action surge It gets fighting styles; but other classes get them at level 2. It gets extra attack at the same level. It gets second wind (which is strong, don't get me wrong: stronger than barbarian d12 HD) but much weaker than Rage or even Uncanny Dodge on a Rogue.
It would be nice (to me) if each of the martial classes fought differently.
Paladin: They have Smites. Lean into it.
Barbarian: Rage/Reckless makes them feel different.
Rogue: Sneak Attack does a good job of making it feel different.
Monk: The extra punch and flurry almost does it. Stunning strike is a bit too spammable.
Ranger: Literally featureless at level 1. Hunter's Mark isn't enough really.
Fighter: Action Surge is the only different feel before level 11.
4e made Rangers feel different with tap-spam. Fighters got a mark and battlefield control.
It could be fun trying to make level 4 martial characters all fight differently within a power budget limited by existing classes (I think Reckless Raging Barbarian with PAM+GWM is the current power budget cap for level 4?)