I'm not keen on private schooling.
My siblings and I went to a mixture and there is no evidence base for value for money nor greater enjoyment nor 'achievement' in our data set.
Our DP paid for private education over and above everything else so we missed out on a lot of other things and the 2 siblings who went private all the way through only got in the housing ladder in their thirties as DP could not help with deposits etc.
For me, private education creates problems as much as avoids them. I don't want my DC out of the house for really long hours and measuring their worth in grades or earning potential. I want my DC to mix with people from very different backgrounds and life experiences, I want them to follow their interests not the interests they're very much directed to have. I want them to feel lucky, content and grateful for their comfortable lives and not constantly want more or the next thing or judge our lifestyle as wanting compared to those with much greater wealth.
My DC mix a lot with privately educated dc and I see nothing that would make me want that for my DC. Their behaviour at sports practice/group activities is not better, their manners are not better, their conversational abilities are not better and their parents attitudes do not make me want to pay to spend more time with them
I was privately educated and would have vastly preferred financial help as a young adult (and more travel and opportunities as a child) and I'm a much lower earner than dh who went to a dreadful comp and is flying in his career.
My DC will be state the whole way and we are on course to be able to support them all through HE and with house deposits.