Classes are weird, but they're even weirder if they're just arbitrary mechanical packages. And they don't have "biological traits" of being wizards etc, but it is that in the setting wizardry is a recognised thing that one can study, and it works in certain ways, thus there is certain commonalities among its practitioners. So one is a wizard same way than one is a doctor.
Except that just doesn't really work. I mean, think about the real world. Doctors are all sorts of things. Some are highly athletic, study BJJ in their spare time, and are world-class triathletes. Some are tubby old 5'1" Italian men, etc. There's NOTHING at all realistic, or even particularly justified by fiction, about wizards that cannot wield swords, assuming they bother to learn how. Sure, wizardry is A thing you could learn and study, but no one thing in any realistic world MUST be the be-all and end-all of your entire existence. This argument MIGHT almost work for wizard, too, being a discipline of which we are free to make up every element as we see fit, given its imaginary nature. But you didn't talk about Fighter, or most of the other classes, for which this sort of logic really just doesn't do anything at all.
Again, I'm not super hostile to the ideas of classes as A) Heroic Archtypes, B) Simple mechanical Packaging for chargen and advancement purposes, C) Cultural ideals existing within the game world to which people aspire. Note that A and B here cannot be relevant to the population in general, and probably not to most NPCs. You could kind of posit C as a thing. Like there's a 'Model Hero' that is represented by each class and thus it is common to see wannabe adventurers emulating one of these stereotypes. Still, emulating and exactly being governed by as a set of rules aren't quite the same thing!
And of course wizards have been able to use swords for a long time. They're generally just bad at it.
I agree, EVEN THE DESIGNERS OF D&D see my point! This was pretty much a free win for them, the wizard can have a sword if he really wants, but since they gave him always-on At-Wills/Cantrips it is an utterly moot cosmetic point (I admit, my dwarf transmuter was actually fairly effective with a sword, there just wasn't much point in bothering).
But I think this is connected to the deeper difference in attitude, which is the role of rules. I think one important purpose of the rules is to tell us about the fictional world and to define it, and you probably don't.
Indeed. I think that's the cart driving the horse, for sure. I mean, it is cool if the rules tell us about the sorts of things we are imagining in our play, but I'm not much on actually defining the nature of the imagining via rules, they have other more effective uses.