Well, I don't think that's an absolute. 4e has rules for applying character classes to NPCs as well (its a bit different from actually doing up a PC, but there are 'templates' for every PC class to apply it to a monster). NPCs effectively have a 'level' (5e obscures this a bit by calling it CR and using a bit different scale). There's no reason to assume that 'Fighter' is a profession (or Battlemaster for that matter). I mean, I'm not in charge of how you conceive of the game world, I'm just saying it is a perfectly valid way to look at it that PCs are unique and the fact that one has a given ability implies NOTHING about anyone else in the whole game world. I see nothing in 5e which undermines that view as a general thing. I get it, traditionally most classic D&D GMs and products have assumed that class levels are generic descriptions. I just don't and I am pointing out that it goes a long ways to solving people's objections.