You don't know what you are talking about, public prayer led by school administrators is banned in public schools in which most children go to and ACLU constantly reminds rogue administrators to fall back in line with the constitution.
The church/state wall of separation is thin and full of holes but is still better than nothing.
When you talk to kids who have been home schooled they are basically scientifically illiterate, many who want to go to college recognize themselves how much damage their parents did to them and their life prospects, the whole home schooling movement is basically an excuse to indotrinate children with superstitious nonsense, exceptions are marginal and irrelevant.
Home schooling completely circumvents the whole point of education, and that is that children should get smarter and more knowledgeable than their parents, this is inimical to the core of religion.
Of course, if we were to restart the whole education thing today with modern technology nobody would even think of having children go to physical buildings to listen someone talk. Everything would be done online with much greater efficiency, much less time spent and much greater retention results, but that's a different story. It still means that you have to have standards for everyone.