That's why I went with a longer stat list in my home brew system. Made more sense to keep stats from doing unrelated jobs. The simplicity of the six stat system is nice, but it breaks the ability to have stats reflect something like a powerful magic user that's also horribly ugly/unpleasant.
Mind you, it also made things get a bit extra when trying to still keep stats to a reasonable list in terms of display on a sheet of paper. Depending on who you ask, that may not have been successful lol.
I really don't like how 5e made all social skills charisma based, too. Like you're always simultaneously good at persuasion, intimidation, and deception. It feels to me like most of the time one of those should be your go to strategy, not pick whatever is best for the moment and you're good at all of them.
I think part of this is a misunderstanding of what charisma actually represents. It's literally just real-world charisma. There are only a couple instances of official materials mentioning appearance as being related to charisma in all five editions put together. Danny DeVito has 18 charisma. Sloth from The Goonies is lovable enough that he's probably rocking a 14 or so. Ted Striker from Airplane has a 4 in CHA. Sure, he's handsome, but he literally bores people to death. Prince Valium from Spaceballs is similarly low, being dull enough that he puts himself to sleep.
On one hand, we have Wilhelm - court wizard, politically savvy, intelligent, keeps a library of useful spells bigger than your mom and never casts the same spell twice in a day.
On the other hand we have Chad Thunderballer, international man of mystique, thrower of nearly infinite lightning bolts, wielder of the forbidden school of Metamagic, slayer of dragons and thots alike. Unless that dragon is blue or bronze.
The rivalry between wizards and sorcerers is well known, but I feel like there should be some more beef between wizards and bards. And sorcerers and bards. And bards and bards.