However, I do not see why an effect that possesses you and an effect that breaks your willpower, like a Dominate spell, would use different saves.
So, the question here, as I understand it, is "why does it look like there are two shots of salvation that represent willpower"?
My answer is brief: they do not.
Regarding WIS balances:
Resistance effects that delight, frighten or assault your willpower
Spell of charm and fears Spells are often from the schools of illusion or enchantment; in other words, they are tricking you into thinking that the opponent is friendlier, more frightening, whatever, than they really are.
They remind me of the fact that Insight is a skill based on wisdom, so it seems to me that resisting charm, etc., is more about being able to see what your opponent is doing and not "falling into the trap".
Regarding the CHA saves:
Support effects, such as possession, that would subsume your personality or throw you into another plane of existence
This moreso resembles the battle of wills with respect to forcing someone to do something or to be transported to another plane or whatever. Therefore, it makes sense that a ghost Possession It would be linked to CHA and not to WIS.
With respect to your homebrew, I would like to go with the quotes you found and turn them into a CHA-based class.
Address the most "severe" spells as Dominate person, that spell in particular says:
You try to seduce a humanoid that you can see within range. […]
While the target is delighted, you have a telepathic link with him …
This still seems more like "cheating" the target instead of forcing Let them do something in the form of a "battle of wills."
But then, it says this:
You can use your action to take full and precise control of the target. Until the end of your next turn, the creature performs only the actions you choose and does nothing that you do not allow it to do.
This, I admit, seems to be entering the realms of the "battle of wills." The best explanation I have for this is that, since the target is delighted, he thinks that the pitcher is a friend, someone he trusts, and therefore will follow the suggestions made, even if these suggestions are so strong that they practically allows the caster to control them like a puppet.
Any additional speculation that I think would go into the territory of "design reasons," so I think that's the best I have for this.