So why can't a high level swordsman have sword forms that are supernatural? You keep saying that these things "need an explanation" but... you just provided that explanation here, didn't you? They learned a technique that isn't mundane. Simple as that.
Ah, I think this answers my confusion from before. I guess you just misread my third question. So, Fairies and Golems are always supernatural. They are also both player options. Fairies were released in Mordenkainen Presents, Autognomes are a type of golem from Astral Adventurers, and Warforged are a different type of golem from Eberron.
But, when I asked if Fighters or Wizards are supernatural, you said that they were mundane. And for the wizard you explicitly stated the problem. You assume that any time we are talking about a Player Character, we are talking about a human. Additionally, you assume that the humans of the worlds of DnD are NOT supernatural themselves. But... is that true?
Humans are equal to any other player character option.. and one way or another EVERY SINGLE player option is supernatural. We don't need a fighter class that specifies that this fighter is supernatural in some way, because the majority of fighters are already supernatural, they are elves, tieflings, genasi, aasimar, golems, fairies, undead ect ect ect. You keep saying that we need to justify why these characters are supernatural... but they are self-evidently supernatural and always supernatural. So, why not assume the humans of these worlds, who are their equals, are also supernatural from our perspective? After all, the game should not need to state that a Tiefling Fighter and the Human Fighter of equal level are equals, that is simply self-evidently true.