I've seen this subject twice in recent weeks. I've never had an issue with Les Paul's (carved tops) staying in tune. Actually just the opposite, they normally stay in tune better than slab bodies.
I do agree with the angle being too severe and being a perfect storm for breakage. I do have a double cut Les Paul (Special, Jr., whatever nomenclature they seem to go back and forth with) that tuning is an issue. But I think it's more of a weak neck mating with the body, than headstock angle.