I've only read the last few pages... My apologies, will catch up later.
Many thanks to those posters attempting to address the huge amount of misinformation about government funding, one of my bugbears.
To answer the OP, there's a very important thing to recognise about wealthy people: they usually live in wealthy areas, and we know that wealthy public schools usually outperform less wealthy ones. So even those who choose their local public school are making a choice not available to everyone.
This is something I hate about the public system. At least with private I can research, question, choose. With public I get what I'm given based on the area I can afford to live in. The more I spend on real estate, the better my children's education.
Now tell me that's not elitist.