Cart Before The Horse
Because people read the stats part of every RPG book first, based on traditional game book organization that D&D originated, they often fall into the trap when they design their first game of thinking that they need to design the stats first and then the rest of the game in section order as they proceed. This is the opposite of the truth.
First you should decide how you want gameplay to unfold and feel like. What kinds of characters do you want there to be? Then create ideas of character types - classes, or point-buy tidbits, or whatever - to match those, then determine what attributes of a character should exist to influence them and by how much.
Some games have no stats, some have a couple (Tri-stat had Body, Mind, and Soul and that was it), some have the "D&D six," and some have more. What kind of stories do you want your game to tell? What attributes of a character are important vs unimportant in generating that? Some games weight stats >>, >, =, <, and << skills/powers in terms of how they affect play.
Your problem is that you are blindly mapping over without understanding the stats you're mapping to and why.
If you have
- Strength
- Mental Strength
- Will
- Agility
- Health
and you want to add in other things to the game, what are they? I'm hearing "divine spellcasting." You could decide that in your world that means Mental Strength, or you could decide it's a Piety/Soul/etc. other attribute to add to the list. What makes a good spellcaster in your divine system? Likeability? Mental focus? Dedication? Emotional intelligence? Book learning? Nothing, it's just something anyone can learn regardless of their personal abilities?
In D&D, is Wisdom a weird mix of sly/common sense/Perception and willpower/torture resistance and Clericyness? Yes. So don't do that if that's not what you want. If you want, as first class citizens, those as two different items, add them that way.
- Strength
- Mental Strength
- Will
- Agility
- Health
- Perceptiveness
- Piety
for example. You don't have to map attributes one to one, I assume someone who has Mental Strength could interpret that as "high IQ" or "lots of learning" or even "determination" (it seems to overlap with Will in fact, without careful definition).
So don't jam your worldview into a stats system, consider what you want the most important aspects of a person to be and have those be your stats. They'll then be working for you not against you.
Ask yourself if there's a meaningful top-line difference between the stats you have - is Body, Mind, Soul not enough and if so why? If something's going to be "dump statted" should it be a skill or something and not a stat? Why do you want spellcasting ability tied to a stat in the first place?
Just wrestling D&D into a different shape without understanding game design will probably just make you and your players sad. Either play D&D, since everyone understands it regardless of how much theoretical sense it makes, or design your own system intentionally to support the game world/playstyle feel you want.
Even if you're wanting mostly the D&D Six, but you're trying to figure out how to change them, this is the process you follow. They dumped CHA because it wasn't used. If you switch spellcasting to CHA you could lose WIS, on the grounds that "force of will" is in Charisma too and you can base saves on it (if you're using that kind of save). In OD&D Wis was the traditional thief dump stat because it drove nothing; it driving perception etc. is a purely 3e+ construct. Or keep it as a spellcasting stat for nature types like druids and rangers (if you have those). Note all the ifs - whether you have a stat or not and what it is should be driven from the rest of your game design.
The History
This actually goes all the way back to the first OD&D supplement, Greyhawk. The maximum spell level a Magic-User could cast was now limited by his Intelligence. Although interestingly, Clerics were explicitly not limited by Wisdom. The justification was that, unlike Magic-Users, a Cleric's spells were divine gifts, not based upon their skill. Intelligence also limited how many spells the Magic-User had.
Speculating, this was probably partly simulationist and partly for mechanical reasons. Arcane magical ability is tied intelligence, both lore-wise and in the the Magic-User's prime requisite was Intelligence. High level spells are more complex (the spell level system is a direct mapping from Chainmail's complexity system) so there's logic to a smart Magic-User being able to handle more complex spells than an average one.
Your Ability Scores had little mechanical impact in OD&D, primarily a bonus to experience gain. Greyhawk began increasing the existing, minor bonuses and penalties and adding new ones. Intelligence affecting Magic-Users spells was part of this increasing affects from Ability Scores. And only Magic-Users with an Intelligence below 11 were actually losing anything compared to the core game, because the 7-9 level spells were added with Greyhawk, and did not exist before ability limits.
This Ability Score limit spread to Clerics with AD&D. High level spells required a certain Wisdom and a low Wisdom could cause spell failure.
You may have noticed that Ability Scores were only limiting the casting of high level spells. As KRyan touched on, this is because of Prime Requisites / Ability Score requirements. RAW, you couldn't even play a caster with a below average Ability Score in their Prime Requisite.
The Implications
So there's the historical precedent, which explains where it comes from. Was there any other reason to carry it forward, beyond tradition? It makes your Ability Score have a greater effect on your casting. The fact that spell strength is often not based on your Ability Score seems like it could be unbalancing to ignore the Ability Score requirement. I doubt it would be that bad, but I'd ask a optimization expert about it.
I personally don't have a problem with the idea that magic is too complicated for the average (Ability Score 10) person to grasp, and the smarter/wiser you are the more complicated spells you can comprehend and harness. It seems intuitive me, but if it doesn't to you and your players, I say house-rule away.
Best Answer
My first encounter with a D&D sorcerer class was 3E. The 3E PHB says on p51:
In religious studies, "charisma" sometimes refers to the inner personal power in an individual, divinely conferred. I had to read endless writings about it in college, especially Max Weber, who described it as:
This is the aspect of Charisma often underplayed. (Also, I am not suggesting that anybody involved in writing D&D had to have read Weber, only that he's a good source for reading about this aspect of it.)
Charisma isn't just good looks or even greatness of personality. There is a sense of transcendent greatness about highly charismatic people.
You'll find more references to this sort of meaning of Charisma on the Wikipedia page for Charisma.