My Dad paid his real estate taxes to fund the local public schools, basically the Putnam City school district in OKC back in the 60's and 70's. It was at one time the largest HS in Oklahoma. He always wanted a tax credit for that since he was paying for me to go to a private school and taking me out of the public school system and the cost for them to educate me. Seems only fair to me, and my private school education cost far more than the real estate taxes he was paying. So, allowing this might open up the private school system to those who might be able to afford it if given a tax credit for the allocation of taxes they are paying in to the public system and in theory the private sector by doing this is helping fund a better education for those who could not afford it dollar for dollar. I don't see this as public dollars, it comes out of the pocket of private citizens. But the government thinks they own us.
This would allow competition between the public and private school systems, and the public school systems would either need to get better, or eventually go extinct. There is no doubt public education is highly inefficient. Over time I believe the private school system could grow to handle a large volume of students and this would happen over time. As for abiding by "public school" rules? Not certain what you are saying because those rules are failing a large segment of the population. If a parent chooses to send a child to a religious or non-religious private school? That should be their choice and religion should be allowed to be taught by those private schools. Private schools have the benefit of having a curriculum that most parents agree with, and if they don't like it they can air their grievances without the DOJ calling them terrorists and this is why private schools should never be expected to behave as a public school. And if a parent can't get their grievances settled? Plenty of other good private schools. In OKC area you have all kids of private school options. Private schools pay their teachers much better, allowed me to have access to college level classes within the HS, private schools are not looking to dumb down curriculum, they are trying to create grads that leave with study habits and a sound educational base to pursue a meaningful degree. They produce more scholarship dollar per student versus public schools.
Public school systems have no reason to improve right now academically and they are being encouraged to do the opposite, and they seem right now to be trying to prove their worth in society by not how well someone is educated in english, math, sciences, trade skills, and PE, but by what kind of a social justice warrior they can produce.
I want more kids to have the opportunity I did and that is not about politics, this is about real education and the ability to have a very robust curriculum and have the ability to become a Doctor, CPA, lawyer, engineer, chemist, architect, professor, teacher, nurse, electrician, I/T developer and other related I/T fields, carpenter, etc...
And best of all? Private schools kick out the kids that hold other students back from being educated because they so disrupt a class room, parent either gets that kid to mind or they are gone. Should be that way in the public school system as well (Obama's 2nd in command in the Department of Education told me I had this right on a flight from Brussels to D.C. but said the US is to weak minded to do it). Education is not a right, it is a beautiful gift that a parent gives to their child, not a daycare center or juvenile delinquent center for the non-violent. You don't value what is given to you for free, you take it for granted.