Not everyone can afford to send their kids to private schools. Also not everyone is qualified to home school their children.
So then it is about economics and not about values?
My parents put me through 12 years of Catholic school and they did it on one blue-collar income. Did they sacrifice to do so? Yes, but they did it because they thought it was important enough to justify the sacrifice. It never even crossed their mind that maybe the government should be subsidizing their decision. My how things have changed.
It depends on what the parent values. I know a guy who sold his house in Florida and moved to Pennsylvania because the right school for his kid was here. He was a handyman.