I think Psionics can be any one of the three mental stats. In the 3e Psionics handbook I think that different contests would test different attributes too. Personally I've always associated will and willpower with Wisdom, Charisma in certain circumstances.
The question really should be why we're making a roll in the first place, unless it's a wisdom save against something else, otherwise it should be our target that makes the save.
I think they did it this way because players would get upset that they have no control over using the Illithid Powers in terms of rolling the die. The target making a saving throw would mean the player has no control whatsoever other than to initiate the mental attack.
I do agree that making it a Wisdom check is weird. It also makes it so that those with higher Wisdom scores have an advantage with the Illithid Powers over those who focus on other abilities. Maybe that's intentional, but it makes it so that classes that don't focus on Wisdom are not as good with Illithid Powers as classes that do focus on it.
I think it should be a flat Proficiency check so all classes have an even playing field. Or... maybe make it like DOS 2's skill system. I Persuade with Finesse because my rogue is good at Finesse and Persuade. Meanwhile, my fighter persuades with Strength because he's good with Strength. In other words, the PC uses the ability they are best at in order to make the Illithid Powers roll, showing that each class channels the Illithid Powers in a different way.
