Um, the idea that backstory might equal proficiency is far from universal. Some games work on that premise, but many, 5E in particular, don't work on that premise at all. It could, easily, but it doesn't. I don't disagree that background could certainly work this way, and probably should for the kind of non-adventuring non-core tasks we're talking about but that doesn't mean it's baked into the system or widely practiced as a general house rule. If you're using the expanded kit plus skill rules that would be a good model, but it's not something 5E does by default at all.