A lot of students would get much better educations in private schools than they could even dream of getting in public schools.
Of course, there would be a process of building new private schools, and there would be some that were, like public schools, of lesser quality at first.
Those would be weeded out by the market system in time.
Everything takes time.
No claim has been made that there would be ubiquitous perfection all at once.
Again, when the bottom line is to make a profit, mass private schooling will produce about the same results we have now.