I am not looking for Superman, the TTRPG.
Aka your not looking for high level dnd.
And this to me is the issue right here. The problem is that dnd is relatively grounded for a reasonable portion of its level range (and very importantly, the level range that the VAST majority of players play at).
The issue always comes as you move into the 10+ level range, and the game changes in scope as the power level crosses a certain threshold. That is the threshold when the mundane must give way to teh mythical. A "mortal man" has no place doing the things that level 20 characters are expected to do or face.
But people don't want their character "forced" into a new mold. I was planning a "mundane fighter" and by gum I want to keep playing my mundane fighter! But the reality is, just as mid level dnd doesn't handle gritty fantasy very well (as opposed to levels 1-2 which are pretty deadly), high level dnd doesn't do mundane....that ship has sailed.
Those levels exist for people to do fantastical, basically supernatural things. And if you don't want that for your game that is absolutely fine, just stop leveling. Again we already know most campaigns stop at 10th level, partly for that very narrative reason. So either start a new game, or keep the game going but stop leveling. 10th is your new capstone, and can be enjoyed while still playing a mostly grounded martial. But if your pushing past that mark, you have to respect that your entering a new phase of the game, and mundane doesn't cut it anymore.
Now I will say that while 4e was terrible with integrating game mechanics with the narrative (honestly I think its signature flaw), this is an area it did very well. The paragon paths in 4e not only providing mechanic benefits as you cross into the 11+ and the 21+ level ranges, but it providing a NARRATIVE package as well. So why is my fighter suddenly turning into this mystical nigh supernatural badass? Well its because:
- Turns out they are a demi-god, and have started to realize their full potential.
- They have become the chosen of god X.
- They have exposed to magic so often its begun to infuse in their body.
Etc etc. So a player could choose their package and it would provide some narrative rationale for why their character is "evolving" as the new tiers are met. This is I think something that all editions could use. Its nice to point out the narrative difference that happens around 11th level and actually make it a conversation piece. DMs should get some guidance and inspiration to talk to their players or include in game how the characters start to change at this point in the game. ITs not just "gaining Xp and get more power" its "you all are starting to peel back the cosmic curtain, and now some things are happening".