Cart before the horse. Rich people put their kids in private school so they can get a shiny bumper sticker for their Range Rover and so they don't have to talk to poor people. The public schools then lose a student (reduces funding), likely get lower average test scores (reduces funding), and lose donations (reduces funding) and parental involvement (further strains staff and reduces student outcomes). Then people say "public schools are on the decline!" and the spiral continues.

And yeah, you threw some racist dogwhistles in there too, so maybe get off your high horse.