I think the post is getting a little derailed here but...
Perhaps the issue I am struggling with is more about design choice: Should equipment be a class feature?
There some good strong arguments here that suggest that it shouldn't be.
I think answering "No" unravels the system as much as it does my brain but it's interesting to think about the classes built without these restrictions.
What would fighter/wizard features look like if armor and weapons weren't a requirement? At a glance, wizards won't change much if at all while fighters (A5e) would need something else to overcome a perceived "deficit".
I think that it all comes down to the concept of classes and how they need to work especially at low levels
A class is a predefined combination of features envisaged to work together to give some kind of iconic, easily recognizable "character type". Makes going in the game easy as it's one single choice (with maybe a couple of options) and clearly visible consequences on the kind of play style, as opposed to a pure classless system where you need to choose maybe several skills/features etc. More beginner friendly if you want.
Now, for that class to work, there have to be some aspects that must be included. The typical fighter probably knows how to use most if not all weapons and armors, so those skills are given to the class as features. A wizard is not expected to do the same, but for spellcasting it's required it can use material components or foci, so that's given as part of the class package.
IMO there's no reason to prevent any character gaining those relatively mundane skills by investing time, money and effort in general, and I don't think it would be reasonable to prevent it or allowing it only as part of multiclassing. Not every soldier has to be a fighter, but they can probably use most martial weapons and armors.
Going back to your question: what would I give the fighters if those skills weren't part of the class identity? Well, I
would give that feature because it's needed for the class to work at all, otherwise you end up with either a broken concept or a forced choice (I have to spend my free skill slots into weapons and armors). If that's not enough, maybe I'd give the class some features that improve significantly the general usage of weapons and armor, so that even if a wizard can wear plate and sword he wouldn't be able to use them as a fighter.
But again, If you think there's no reason why any character couldn't learn those same fighter tricks (I do) you're moving away from a class based system towards a more general skill/feats base system. I wholeheartedly prefer the latter, although IMO A5E does a great job at the former
