While I agree that banning legacy preference is good policy, how do you prove a violation exactly? And who is gonna do the proving?

If you want to make this work, and you should, you need to do something like total application anonymization, which means identity can't be deducible from any application materials. This is doable with standardized tests, which are a good approach to solving the admissions problem anyway.

So, college admissions should be based solely on standardized test scores.