Public education should be abolished

Lastly, this claim: "We've got nothing to lose and everything to gain by privatizing education." is completely the opposite. We have everything to lose and nothing to gain by privatizing education. Privatizing education means turning education into a for-profit service for those that can afford the private services. K-12 education would become nearly inaccessible to poor people, even worse than how inaccessible higher education is today. A superior quality of public services is it's universal accessibility to everyone, which private services fundamentally fall behind at (especially in your world, where you admitted to believing that private establishments should have the right to discriminate if they choose so, thus our society's education system would further degenerate into it's pre-Civil Rights era of segregation and sexism). Another reason public education/services are superior is that they are structurally more accountable to the communities they provide for, whereas private services are definitionally private and accountable only to themselves. Private education establishments are able to choose their own curriculum, and can include or exclude anything they wish, without any real obligation for the students, parents, or community. Private schools can teach things that are blatantly false, like creationism, and exclude real science, like evolutionary biology, without any accountability. Society would become dumber and more discriminatory, as well as further wealth inequality...there is no benefit to such a society.