Currently 5e has 3 Full Charisma Casters, 2 Full Wisdom Casters and 1 Full Intelligence caster. (There is also one half caster of each type). I feel between Intelligence, Wisdom and Charisma, Charisma should not be the most common; if anything it should be the most rare. (I know that the two spell-casting subclasses use INT, but I rarely hear anyone talk about these, let alone use them.)
Charisma, in my opinion, is the most powerful mental stat to be maxed. Currently, however, it is entirely possible to have a party diverse enough to fill all roles who are all based on Charisma. Charisma measures the force of ones personality, and I feel that spell-casting from one's personality alone could be something very special; however it currently feels overused, as does an especially high Charisma stat in typical 5e play.
Fix A - I feel Charisma is so intrinsically tied to the Bard that to make it use any other stat feels wrong. I feel Warlock could be changed; while I like the implied flavor that how well you cast is based off how much you can convince your patron to give, it is not a huge part of the classes identity. I could theoretically see Warlock as a Wisdom class, but I think it would feel too similar to cleric. I think the best change for Warlock would be to base spell-casting off Intelligence. The implied flavor would be through studying their patron, they are better able to harness the magic associated with them.
Fix B - Sorcerer is the other class which could theoretically give up charisma casting, but I would much rather change Warlock and call it a day. However, I feel Charisma shouldn't have to be intrinsically tied to the Sorcerer's identity. While I get the implied flavor being the Sorcerer must have a strong will to harness their dormant magic, that could just as easily be describing Wisdom. In a vacuum, what makes the most sense to me would be to make the Sorcerer become the first and only Constitution caster. (In a vacuum) the flavor matches up, and having their spell-casting be an already important ability would free up space to pump up another. I can see how in actual practice this could be a problem, and to counteract some of this I'd replace the concentration system with an overload system for Sorcerer (think in video games where if you shoot too fast the gun overheats),.
Fix C? - This one feels a bit unnecessary, but I figured I'd mention it. Paladin could be switched over to Wisdom, both making it feel more like a divine caster. The flavor also makes sense to some degree; Wisdom saving throws are typically made for one to retain their will, and that is more or less what paladins are all about. Again, I feel like an unnecessary change, but it was still relevant to the discussion.