Originally Posted by
NichG
The OP explicitly mentioned shonen and changed the thread title to say 'high-powered fantasy' rather than high fantasy, so the implication to me is e.g. the stuff going on in One Piece, Naruto, DBZ, Bleach, Jujutsu Kaisen, One Punch Man, Fairy Tail, Random Isekai Anime #47, etc. Also, I would agree with the other poster who gave LotR as an example of low fantasy rather than high fantasy. Magic is not prominent in day to day life in LotR. It's closer to Conan than it is to, say, Forgotten Realms even, much less something like Fairy Tail or Slayers.
My point is though that 'just run it and it can be as epic as you want' isn't really good advice when very few people will actually have any idea how to conceptualize those sorts of things in the context of a D&D game. It's all well and good to say 'the DM is part of this process of making it possible', but the OP is asking 'okay, but how do I actually DM that in practice?'. And my answer is, establishing expectations with the players as far as what they can reasonably do and then have them progressively test their limits and find that, consistently, they can go beyond them.
Just being like, well, if a PC tries stuff I'll let it work is only half of a recipe. The other half is making sure the player knows that it's worth trying, and establishing expectations like 'what does it mean to be high level in this setting?'. You mention how far apart the goal posts can be - that's kind of the point. If you want to run Daily Life of the Immortal King and your players think they're in Shokugeki no Soma, it doesn't matter if you jokingly let each player write a single infinity symbol somewhere on their sheet - they need to know what sorts of things are reasonable to do with it.
Even 'consequence free Wish' won't do it if the player using Wish feels they're in a normal campaign with normal limits to what they'll be allowed to actually get away with. You would have to show someone e.g. using Wish to reincarnate into their past self and get a do-over of their entire life, or using it to raise a continent from the ocean floor that they suddenly become the ruler of a nation of amphibians or stuff like that to drill in the point 'yeah, this is just the kind of thing that high level characters do before breakfast in this setting'.
As a less open-ended suggestion, play 3.5e D&D with the BESM Advanced d20 Magic/Slayers d20 rulesets (doesn't have to be in Slayers as a setting) and compare to baseline D&D. If you thought 'wizards are broken' was a meme of baseline 3.5e D&D, you ain't seen nothing yet. Though in that system, fighters with a single wizard level make better wizards than wizards...