Well, I do think there's something in this OP.
My DH and I thought about selling our house and moving to a small flat to send our 2 boys to private school on sports scholarships and bursaries. However, after much thought we decided that the assumptions made about them and expectations would not be what we want for them...
If they get good grades from a state school -"oh they worked hard, well done".
If they get good grades from private - "well, of course, their parents paid for that".
If they get to a good uni from state school - "well done for all the grafting"
If they get to a good uni from private - "boys club, always the same, everything handed to them..."
If in the future they decide not to be academic, from state that's acceptable, less so from private ...
If in the future they want to go into politics, senior leadership etc... Companies might be more inclined to take from state. If they did take from private it would be "oh always from private schools..."
The list goes on ....
I think if you are ultra rich (I'm talking royal, celeb, etc..) then private school.is worth it as there is expectation on you already, and you can be protected to some extent being around others in privileged positions. For normal people, I just think nowadays private education is more of a disadvantage.
I want my children to feel and be seen as working for where they have got, grafters, deserving.
If they went private, even if this was all true (ie. They worked bloody hard, grafted, deserved what they got) to many they would just be seen as privileged with everything handed to them on a plate.
One of my children does an elite sport (swimming) and I have already noticed that most of the elite sportspeople in his field are from private school. Even I am feeling "bloody hell it's not fair, of course they will be more likely to get to the Olympics if they went to millfield, had their own pool etc..." The people I most respect are the adam.peatys, who were successful despite everything. As much as I'd love DS to have the advantages that private schools bring (professional swim.coaching on top of being a regular club, access to excellent facilities, acces to great eduction etc. Etc...) I don't want him to be viewed as only making it because if that. I want him to be viewed as making it despite lack of that .... (I know which is better for self esteem and expectation too)