Warning: Ramble.Depends on what you mean. If you're doing it like One Piece where obviously impossible abilities still aren't magic because they don't run off of any identifiable phlebtonium, that does work.
However, that other stuff you mentioned is simple low-grade action movie bullshit. Namely, the hero can do improbable things (such as have a million bullets in a row miss him) but he can't do impossible things (such as survive being shot directly in the heart with a harpoon). That's still a problem, because at higher levels you explicitly need to do something that's impossible to advance the plot under your own power
I don't watch a lot of anime these days and I have never seen an episode of One Piece/Naruto/Avatar so a lot of those type comparisons are lost on me. That said...
could describe like EVERY ANIME EVER. Even the "realistic" ones. And yes, that is fine by me. As long as the game is not set on the earth, I think the ideas of Fighters being able to eventually jump so far and so fast that they are essentially flying is fine. No explanation or rationale should be required, any more than for a wizard's spell. But I would prefer that the flavor text remain that 'it's not magic, he's just that good'.where obviously impossible abilities still aren't magic because they don't run off of any identifiable phlebtonium, that does work.
Anyway, even within action movies there are tiers. John McClane James Bond could beat a wizard. It doesn't matter what the wizard does or what fucking retarded "game-breaking" powers he has. James Bond is a badass normal to the nth degree. James Bond always wins. I know that makes James Bond a pretty nonviable PC/Character Class. But in any case, I don't at all agree that the badass normal has a shelf-life of Level 5.
(In the above paragraph, replace James Bond with Batman if you prefer, unless it will lead to 'Batman is a gadgeteer' argument.)
I think I would have a different approach to fix this problem because I think the actual cause of the problem is the GOD DAMN MULTIVERSE. In other words, 'GO TO HELL' should require a quest or a plot device, not just a class ability. And if it is a class ability, it should be one that every class gets at the same level. But having it be something that NO ONE can just 'do' is much cooler.John McClane might be able to kill a thousand terrorists, but none of his abilities do a damn thing towards helping him with the 'travel to another dimension and kill the hell king' plot unless you offscreenedly buff John McClane, nerf the unassailability of the adventure, or he gets the keys to the plot handed to him.
Basically, a lot of the reasons why "fighter-types can never be as cool/relevant/neato as wizard-types" arguments seem to boil down to 'because they cannot go to GOD DAMN OTHER DIMENSIONS'. I think, if we can't get rid of or downplay other dimensions (which is my preferred solution) or make it so everyone becomes an MtG Planeswalker at Level 20 by virtue of being Level 20, and before then everyone including the damn wizard needs some kind of plot device to go dimension hopping, that is a better fix than anything else.
Of course, this is all a subset of
I think that outside of dimensional travel, you don't need such an 'everyone gets nice things or noone does approach'. Being 'better/faster/stronger' is a nice thing in-and-of-itself.MAYBE THE WIZARD SHOULDN'T HAVE THE ABILITY TO DO EVERYTHING