1 the state does not fund their education. They are privately wealthy (and yes, lots of people have a problem with that but if you're going to get upset with them for private wealth, I assume you're planning on handing back that house you would have inherited when your parents die?)
2 I assume they'll now pay VAT too. Excellent news.
3 Most private schools are significantly smaller, with significantl more resources, and a much higher ratio of teacher to student. This is a huge benefit in the case of children who are genuinely at risk and whose parents must, in 2024, be terrified of the increased risk of social media and the like and what that could mean for their children innocently taking part in a school production, a class discussion or changing for PE.
4 Other royal families may sometimes use some state schooling, but actually, they often send their children to other countries (the UK in particular) where they are often largely invisible. There is significantly less press intrusion etc. The British Royal family is, without a doubt, the most high profile royal family on the planet. In addition, if the royals tried a similar thing - eg sending the kids off to school in another coutnry to sort of remove them from the craziness here, the screaming and yelling "is England not good enough for you" would be insane.
5 Security at private schools is already a nightmare in the context of the royal children. It would be 10x more complicated at most state schools which are significantly bigger and more crowded.
6 Agree or disagree with the existence of the royal family as you like, but at private school they are far less likely to be targeted for being super wealthy super privileged etc. At the local state, there will be a lot more families who will have ethical and moral issues with them and will be quite happy to make those clear to the children in person.
7 if they go to state school, there will be lots of whining about them taking up places that could be used by other children