Who's gonna switch to 5.5, and why?

[Arkhios]

However, I do believe that higher-level characters have to have something along those lines (being destined for great things, unnatural luck, etc), even if they lack explicit superhuman powers. And it'd be even better if the game just acknowledged that a level 11+ character can at the very least make problems for things that can threaten kingdoms or even worlds, through sheer personal power.

Well, level 11+ character is much more likely to have access to supernatural resources such as spells (Magic Weapon, or Elemental Weapon, for example), quite possibly their own, even, so that's one way to acknowledge it by RAW. Class abilities are another way.