When I see "Guy at the Gym Fallacy," it normally reads to me like an argument against the "Captain Hobo Problem". As someone who prefers martial characters, this always strikes me as telling me that I am having badwrongfun at their expense.
Spoiler: Captain Hobo Problem Definition
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Captain Hobo Problem
A theoretical character in a system which generically surcharges game effects based on their utility and directs the player to fluff their effects post-hoc. He's used as a shorthand for the dangers of assigning weak fluff without regards to its relative in-game effect; Captain Hobo's super-speed is described as being the side-effect of 'too much energy drinks and vodka', his 12d6 attack (the max he's allowed to buy out of chargen) is a broken chair leg, his toughness is described as 'layered clothes from Goodwill with cardboard and tape', etc.
The problem with Captain Hobo is that merely by existing he makes everyone else's character less cool. Your badass magical martial artist with mastery over the four elements is only as effective at superheroics as a drunken smelly guy. A less extreme but no less illuminating example would be someone playing a James Bond clone whose PP7 could do more damage than the mortar shots of Artillery Man or someone playing a Conan clone who could outwrestle someone's Superman expy.
Stop by Linear Warriors, Quadratic Wizards and Magician Superhero Problem to see what can happen if you naively attempt to avert the Captain Hobo problem.
Ok, I got one for you: Why is it (virtually) impossible to kill a hill giant by falling damage? Regardless of the height, the odds of a hill giant dying from a fall are significantly less than one in a million, yet from everything we know about physics, a larger person should be significantly more susceptible to falls from extreme heights than one of ordinary size.
Is the hill giant super humanly tough?
If so, then why is a super humanly tough fighter killing a super humanly tough giant any easier for you to believe than an ordinary fighter killing an ordinary hill giant?
From my perspective, you are removing character options from the game while I am trying to add to them.
A monk is someone who uses chi to enhance themselves and reach a state of perfection that transcends humanity. Fighters are masters of armed combat who utilize tools (usually magical ones) to enhance themselves beyond what is ordinarily possible.
If you want to merge them, D&D has you covered, multi classes exist, so do sword sages.
But by saying that every high level fighter has to be more than merely human and able to perform shonen style feats, you are mushing together two separate archetypes and telling people who want to play the pure thing to take a hike or stick to the kiddie table.
Again, this is just how I hear it, not some statement of objective fact.
Stating that D&D is a high fantasy game not a super hero game isn't really me stating a preference, its an objective fact. Just google D&D and look at the first summary that pops up, and then do the same to Champions or Aberrant or Mutants and Masterminds.
It is mostly a narrative thing; the idea of someone who has to overcome hardships to defeat a great evil is to me much more compelling than a demigod smooshing everyone who doesn't agree with him. Batman beating up Bane seems heroic, Superman beating up Bane just looks like a bully.
From a mechanical perspective, I would like everyone to be more or less equal, but if there is an imbalance (and there will be) I prefer to be on the weaker side of it. D&D tends to already have a mechanical bias against non casters, I don't see any reason to compound this by capping them at low level.
Ok, so Super Heroes typically have powers but not always. Let's get away from that term then. What I am saying is that D&D typically models itself on stories where the majority of the characters are more or less ordinary humans like Conan or Lord of the Rings, while a setting where the everyone (who matters) has super powers will start to resemble a different genre more like something you see in superhero comics.
I wasn't there, but both of those examples all sound like a DM just trying to play by the rules and comic up for reasons why you couldn't just bypass the mechanics for disabling devices rather than an active attempt at limiting martials.
As for the Reddit story, that just sounds like a jackass DM. There is no excuse for being a stickler for the rules when it comes to martials but letting magic users ignore the rules. Also, I am pretty sure a "guy at the gym" could run 25' in 5 seconds and could easily bullrush someone through a glass window.