I would be happy to pay more yes – thanks for checking. My tax also pays for many state and council services that private school kids and their parents benefit from, so let’s not start making silly statements about that.
You know you actually can make voluntary, additional tax contributions? You can just bank transfer direct to HMRC. Why not do that when you can apparently easily afford private school, instead of expecting private school parents to do it for you? Maybe also get all your friends who can also easily afford private but choose state instead, to join in too!