That is a false assertion. Colleges have massive economic power, wealthy donor bases, lucrative TV contracts, and a need in a competitive environment show their schools in the best possible terms to attract the next generation of students. All the same things that power many, many rich coaches and administrators to get paid off the labor of poor often minority ethnicity kids.
I think what this would do is take that same money, and redistribute it to the players who actually produce the product on the field/court.
Would there be change. Yup. Some schools would self-select out of the arms race, some would choose to invest at a lower level and come up with different strategies to compete(pay coaches less, spread less money to a more even group of talent, increase other benefits, etc). Some schools would burn through all sorts of cash on their staff and less on players, some would choose to operate at a loss, some would choose not to. Some will offer 2,3, and 4 year contracts to marginal prospects to get an advantage over higher offers at a single year. In short, it will be a burst of new opportunity and change, but not the "end". I will always bleedblue because I attended UConn.
I think it would be really interesting actually. And of course it would be a much, much, much more just system. Which is really the point that matters.