"Public" does not mean transparency here. It means that it is paid for by our taxes.
"Private" means it's paid for entirely voluntarily by people who find value in it. Transparency might vary, but no one forces you to pay for it.
You sound like one of those teachers insisting on 6yr olds choosing their own pronouns the first day of school. It would be very worried if I was forced to send my kids to your class every day. Thank god we still have other choices in this country.