Hot Take: Wizards' power should scale more from Wisdom than Intelligence.
Maybe. I'm not 100% convinced. But given the historical tradition of the clergy as the educated, monastic, institutional class and sorcerers as the mysterious, outcast, freak class, I'm inclined to base Clerics on Intelligence, and Wizards on Wisdom. There's decent arguments against this (and really it should scale off of both but that's a level of crunch nobody wants to deal with), but we're going to roll with it.
Anybody can cast a spell. It takes time and knowledge and effort and you might mess it up, sure, and those who carry around ancient tomes full of spells might well be wizards, but merely spellcasting does not a wizard make.
What makes a wizard? Secrets. Insight. Perceiving reality as others do not. Seeing that which others cannot. Wisdom.
With that in mind, here is Wisdom for Wizards:
You are as perceptive and observant as an ordinary person. You know that which an ordinary person would.
You can always remember your dreams.
You know when you perceive a lie, be it written or spoken. When you meet someone, you instinctively know one secret about them.
You can speak the secret language of birds; if properly bribed and persuaded, you may be able to recruit spies.
You can see through illusions, and can see invisible things.
You can see ghosts, faeries, demons, angels, and spirits. Each of those—whether others can see them or not—will sometimes tell you things they wouldn't others.
You can also see DEATH. When you die, he'll come to collect you personally.
You can read all written text, no matter its language or script. You know the secret language of runes.
You can see the true forms of shapeshifters and the disguised. If they have multiple forms, you can see one form in your left eye and one in your right.
If looking through a mirror or lens, you can see and speak into other planes of existence, like Hell or Fairyland; assuming there's someone there, they can see you and reply in turn.
You can see into the future. If you keep your eyes closed for more than a minute, you will start to see fragments and snatches of what will, inevitably, happen to you. The visions may be unclear, but they are always accurate.
Any question you perceive—through sight or sound or another force entirely—you know the full and complete answer to, whether you want to or not.
There maybe should be some hits to your CHA or INT to go with this, but whatever it's fine.
It's etymologically sound, nerds.