But only having sword-lile technology instead of having other options that are more advanced is also setting specific. Only having the weapons that are in the PHB and nothing better right now is a pure setting decision.
And like for me, in a medieval life fantasy setting with the technology that is shown in the PHB it makes absolut sense, that non magical characters will be weaker and left behind by magical characters. Because Magic for me is just another form of technology. And the non magical tech in the generic 5e D&D setting doesn't allow nonmagical people to compete with high level wizards/spellcasters, which is something I'm totally fine with.
So, the nonmagical martials/supportclasses either need to get their hands on magic or they need to advance their non magical technology.
I personally wouldn't like Anime/Manga Protagonists who just trough mundane training become as good as a 20th level wizard. That just feels wrong to me and I wouldn't want that in my game. If you have a supernatural explanation for their super strength or abilities, it is fine by me (so like One Piece is better than One Punch Man).
Even in the super hero genre if you want super powers you need to get hit by gamma radiation, take a "magical" serum or drug or build a suit or something.
Like Batman. In a fight with superpowers villains he isn't punching them super hard. He defeats them with planning, gadgets and often super powered allies.
Or Tony Stark. Without his suit he is just a more smarter, nicer, better looking version of Elon Musk.
And I think a lot of people think like me (at least in the West), that unless you have tech or magic/supernatural source, a mundane person, no matter the training, should never be better than somebody with magic/tech/supernatural abilities in direct competition. Should the mundane be able to defeat the super natural? Of course. But not trough brute force but trough cunning, planning and passion. Like Batman does.
But if you want a level playing field, where a mundane person goes toe to toe with high level supernatural beings like Wizards or Hulks, you need an Iron Man suit or the fantasy equivalent in my book.
Because in my fantasy worlds, the abilities of mundane folk compares to Frodo, Bilbo, Boromir, Aragon, Gimli, Legolas and not One Punch Man or Kirrin from Dragon Ball.