Price discrimination in the form of scholarships and the "show us exactly how much money is in your wallet" scam they call "need-based-aid" allowing universities have essentially perfect price discrimination and to gobble up the entire consumer surplus is definitely a big part of it.
Imagine any other service where they demanded your bank statements before they told you what they would charge you, and the impact that would have on sticker price.
Imagine any other service where they demanded your bank statements before they told you what they would charge you, and the impact that would have on sticker price.