I would consider the "mismatch skills with abilities" variant rule a little more than just a variant rule given that it is clearly how the designers actually wanted proficiencies to work, given that "pick the appropriate skill and add proficiency bonus" is the approach they took with proficiency in tools, musical instruments, vehicles, etc. The pull towards having set skill bonuses already added up on the character sheet is just too great though, partly because the skills they chose did mostly each sit comfortably with one ability, partly because of the way the character sheet is set up, and partly because the "floating proficiency bonus" concept just doesn't quite click with a substantial chunk of players (in my experience the majority).
Having just spent several weeks helping little kids play D&D I will say that part of the problem is that the name "proficiency bonus" sounds way to technical and is something most kids (and probably a lot of adults) just don't want to tangle with to the extent they can avoid it. In this age of D&D Beyond auto-calculating stuff and most groups having someone reasonably knowledgeable willing to help anyone update a character sheet on that rare occasion when the proficiency bonus changes, getting by without actually understanding the proficiency bonus is pretty easy.