I think that wisdom should indicate a person's insight and awareness. Charisma should estimate a person's magnetism, looks, force of personality, and ability to influence and be influenced by others.
If a spell or effect attacks a person's willpower or consiousness, I think it sounds like an attack against their ego/sense of self/strength of mind. So, would it be hugely game-altering to have Cha be the ability tied to will saves instead of Wis?
What would be the undesired consequences of that houserule?