Mercurius
Legend
I share your dislike of bad accents, although probably for different reasons. I just find them silly and annoying, especially if done poorly. I've had the same thought about why is it that almost every fantasy world, as depicted in film, involves people with British accents? It gets worse when a random thou or doth is thrown in.Solution: Don't adopt ridiculous voices. At best, it has no real purpose in-game. It doesn't add verisimilitude. And at worst, you're perpetuating stereotypes and being kind of a jerk.
DMs - talk to your players about not caricaturing (and try not to do it yourself).
Players - maybe talk to your DM about talking to the players about not caricaturing (and try not to do it yourself)
On the other hand, there's the opposite problem: fantasy people speaking as if they're contemporary people, whether American, British, or whatever. In that regard, I think both Game of Thrones and LotR did a good job depicting characters that seemed inhabitants of their worlds, and that's partially because both involved actual dialogue from the books, and Martin and Tolkien are/were master writers.
But I don't think a bad Scottish accent--or really, most of the time, a bad vaguely/quasi-Scottish accent--is cultural appropriation in any sort of meaningful or harmful way, especially in the context of a game group. I see it more as sloppy and unimaginative.