My character is nothing. My items are everything.
Items in fantasy fiction are often
part of a character.
Hell, it's trite enough that kid's shows featuring powerful characters will often have an episode that is explicitly "I'm heroic because of how I use my powers, I'm special because of who I am, and my magic rainbow wand or sword of destiny or whatever is useful for my goals, but in the hands of someone else, would be nothing (or even destructive)."
It's also true about spellcasters that
they are nothing special without magic. Without the "spark" that lets them do fantastic things.
And hey, I'm perfectly fine with giving every PC fighter a bloodline and destiny as part of the kit. I've been perfectly willing to make every PC fighter a chosen one hero/villain imbued with supernatural power. Make them all Percy Jackson. Let completely normal run of the mill warriors be NPCs. Every PC class should be special by default. Everyone wants to be Superman, not Jimmy Olsen. The amount of mundane options in 5e fills a thimble with room to spare. Get rid of that and you add so much more design space to work with.
D&D already kind of works like this today (NPCs aren't fighters, they're veterans or warriors or knights or...), so this isn't even a big leap. It's a question most D&D characters should have an answer for at some point: Why are you just
better than most people? What makes you so special?
I'm OK with that answer being delayed 'till about level 5 or so, when the distinction between a PC and the rest of the world becomes basically undeniable.
Trevor from the first anime is a pretty good example of the "not obviously supernatural" warrior, although he's definitely supernatural in what he's able to accomplish. The whip plays a role, the Belmont bloodline probably plays a role, but his powerset is mostly defined by being a badass.
Sure, but he's not adventuring alongside characters who can grant wishes once a day and teleport between dimensions if they want to and raise the dead. His supernatural-ness is subtle, but nobody in his party has abilities like high-level D&D spellcasters do. It's not a party of demigod-slayers...the magic the casters have is not that powerful. The flashiest is probably the summoner, but "make a bird claw your face" is not the same impact as even a mid-level D&D spellcaster.
There's a lot of unstated "magic is just too strong" in some of the martial/caster angst, and that's a fundamentally different argument than "martials are weak."
There's also a bit of "D&D should probably cap out at about level 10 anyway" hidden in there, which is also a fundamentally different argument.
Neither of which I really disagree with, tbh, but those both require different design fixes than just amping up martial power.
If the only change we made to the game was that it now went 1-10 and 5th level spells are the max power level (maybe with some optional higher-level add-ons), we might still have the issue, but I bet we'd have it mitigated significantly. Even more so if the game went 1-5 (which is still about 4-6 months of gameplay, so not even a small amount of real world time).