Instead of need-based aid, try need-blind colleges.
https://en.wikipedia.org/wiki/Need-blind_admission
What are you talking about here?
Need-blind admission would be "we'll make the decision of whether to admit you without considering whether you can afford to come". It's analogous to an iPhone offered for sale at $1000, even if you can't afford to pay $1000 for an iPhone.
Need-based aid means charging less money to people who, in your judgment, can't afford more. It's analogous to finding scruffy people on the street and giving them 70% off coupons for iPhones.
There is no logical dependence from one to the other. An Apple store does practice need-blind admission, and definitely does not practice the "required" need-based aid.