I find that, as an over simplification, many RPGs fall into two broad categories.
One, which includes every edition of D&D is basically Zero to Hero. The advancement has huge effects on what you can do, and the game is designed around challenges at all sorts of different levels of character power.
The other category, exemplified by systems like superheroes in the Hero System, have a slow rate of change. You get mildly better over time, or get some new power stunts, but there is no dramatic changes. Foes that would have cleaned your clock a few months back aren't a reasonably fight now, and just fodder (if you ever seem them again) a few months in the future.
So for D&D, I am sure you can tell a great story at a set level, but you are cutting out so much of the content. Higher level foes, higher level spells, the works. So I guess that a DM I trusted could convince me to do it for a particular game they have a strong concept for, but it wouldn't be my default way of playing D&D.