The other half of what I'm arguing against (that half we apparently agree on) is the idea that staying in lane would be anything other than a bad thing. That it fundamentally doesn't matter that the players pick and choose the parts of the fluff that resonate and the game is better for it. If I want to play a wizard but prefer the mechanics of the warlock (pact of the tome/Book of Arcane Secrets) I'll have a better experience taking that guy as a wizard than I would if I had to juggle slots and spell levels.
I think that in reality this kind of thing - i.e. re-skinning a class to represent something it isn't, particularly another class, is both rare enough in practice, that it doesn't really matter,
and more importantly would happen
regardless of whether the classes were worked into the world, because to do what you're describing means you're already ignoring the lore associated with the class.
A point was made earlier that one player might be totally into a their Druid (or w/e) as part of the world, and another player might be a Fighter but be all about the character who he isn't particularly classically "Fighter-ish", and I think there's a bit more truth to that, rather than the notion you have here. But that doesn't really mean that you can't have classes that are part of the world.
I mean, having read Worlds Without Number recently, I'm increasingly leaning towards the idea that you could mix more specific diegetic and more generic non-diegetic classes, so long as you relatively cleanly delineated them, and WWN also shows you could freely re-skin the diegetic classes, them existing diegetically as part of the world is absolutely no bar to that.
It's notable that D&D basically already has a diegetic/non-diegetic split, and it's basically "who has magic powers and who doesn't". If you don't have magic powers, you're non-diegetic. If you do, you're diegetic. This is generally reflected in settings, which often spend some time situating magic-power-havers in the world, particularly full casters, but relatively little on martials. 4E was the real exception as just about all the classes were equally diegetic/non-diegetic. 5E feels largely like a return to the older approach, slightly confused by the fact that more "martials" have actual magic powers. I think 5E is slightly holding back the remaining martial classes by keeping them non-diegetic yet also non-generic.
One additional point I'd make would be that if it wasn't for Vancian casting, the specific scenario you outline would likely never come to pass. D&D's lack of a developed alternative (Warlock being the closest we have right now - spellpoints being underdeveloped as an option) to Vancian casting is the source of a lot of the woes it has, class-wise, frankly.
Personally, I think I prefer games to be free form like Savage Worlds or games in which the available classes ARE diagetic. D&D is coming across as a mix of both, which is confusing to me.
I don't find it confusing, personally, but I do think the game would be better off making a clearer decision. None of the arguments to the contrary seem particularly convincing. To whit:
"It's why D&D is so popular" - This is an argument as hollow as a maraca. There's almost nothing it's not applied to. We've seen it wildly applied to different aspects of D&D over and over, particularly in the last few weeks. It's basically a kind of logical fallacy, because there's never any particularly strong argumentation to support it, just an assertion that obviously it is the case.
"We need to be able to re-skin classes!" - This is possible regardless of whether the classes are diegetic or not. But I would argue that having a default position of making them diegetic would be helpful to a lot of players and also helpful with some worldbuilding.