I think it trivializes the idea of backgrounds and just makes it a bundle of characteristics with a collective label on it. If every background comes with a bonus language but they’re going to say “well of course you can swap out anything you like in your background if you decide your Guard doesn't know Dwarven,” why not just say everyone gets a bonus language, pick one? Why bother tying it in to background? They’re just saying “pick another language” in a more complicated way.
I think it would be a lot easier to say something like “everyone gets their race’s language and common, plus a number of languages equal to your intelligence modifier.”