Charisma as a casting stat associates magic with your person.
The magic of clerics does not arise from their person.
Clerics, for all intents and purposes, are tools.
There is no barter, exchange, swear or oath.
They are simply vessels, conduits.
They are selfless in that regard.
Charisma, as it has been presented, is an awkward fit.
Why can't charismatic people be selfless? What does that have to do with selfishness versus selflessness? Many highly charismatic leaders of the world have influenced others to be more like them by harnessing the power of their own force of personality to further altruistic goals greater than themselves.
Also,
in your opinion, the magic of clerics does not arise from their person. Gods differ, and there are quite likely many gods who chose the vessels through which they channel their power based on the force of that individual's personality. The ability for that individual to successfully bring to bear said force of personality to enact change on the world is quite likely to be appealing to a great many divine beings who wish their goals to be furthered.
Moreover, all spellcasting stats associate magic with your person. Intelligence is the harnessing the power of your own mind, focusing its ability to understand the knowledge being presented, to recall information you've been previously exposed to, and to make intellectual leaps as you logically come to a conclusion based on your preexisting knowledge. Wisdom likewise relies on the power of your own mind, and your ability to use the knowledge you do have in the most efficient manner possible (and wisdom really likely shouldn't be its own stat, since wisdom is definitionally knowledge + experience; anyone can acquire wisdom, and most people do acquire wisdom as life goes on, through their experiences). Charmisma associates your magic with your ability to perform, to project your will onto others, or the strength of your convictions, the simple ability to believe in yourself.
As for the assertion there is no oath, no swearing? That I flat out dispute. Countless religions, real and fictional, require followers to swear their loyalty, their devotion. Both in their hearts, one on one in communion with a deity, and also explicitly reciting ritualistic oaths affirming said devotion both in the eyes of those gods and in the eyes of their fellow worshipers. Some specifically require such oaths when formally taking the vestments and position within the religious organization, the oath of a devout follower swearing their service to their god.
Yeah, the more this thread goes on, the more I am coming to the conclusion that wisdom likely shouldn't be a stat at all. Perception makes no sense as wisdom. Telling animals what to do makes no sense as wisdom. Medical knowledge certainly makes no sense as wisdom. Insight makes more sense as a charisma skill, since the basis of the charisma of many people is their ability to read the cues of others and play off of them; insight is intimately tied to charisma, and few are the truly charismatic people incapable of reading others either intuitively, or, more rarely, through specific training. No, wisdom is in no way specifically tied to intuition. Some people are intuitively more wise, certainly. But a great many people are wise because of years of experience combined with their own knowledge.
Intuition should be a stat, far more than wisdom. The ability to intuit is a bit more separate from intellect. And perception should be its own thing. Perception is only sometimes the ability to use experience to know what to look for. A lot of perception is based on sensory acuity, or raw intellect allowing you to sort through the sensory data being gathered at a faster speed. Much of it is flat out based on having superior physical senses; a better sense of smell, better hearing, better vision.