What even is armor proficiency?

[Psyren]

My problem has always been that proficiency feels too much like a game abstraction. Like, imagine you have a perfectly normal gun, and you have extra ammo, but the (hypothetical) rules of the game only allow you to reload on a short rest. So how do you roleplay running out of ammo in the gun? The game might be balanced around it, but it would still feel super weird.

It's a magic gun, as are the vast majority of "recover on a short rest" abilities. Yes, that includes things like a Fighter's Second Wind or a Dragonborn's breath. How it works in the fiction can therefore be as arbitrary as it needs to be.

*snip*

When someone suggests you put on some armor before a big battle, "Oh I'm not trained to fight in armor," is not a response that makes logical sense, not for a career adventurer.

It is if you have alternate means of getting decent AC, which every adventuring archetype does. If I'm a wizard and I'm not trained in armor, but I know the mage armor spell... why wouldn't I just use that? Sure there are probably other wizards who would delay their magical training to learn how to use armor properly, but not everyone would go that route.