Interesting debate!
I had 3 kids in 4yrs so would always be a triple hit for about 15y from Yr7- end of uni, so that's a big factor
I went to state schl snd so did DH and all my uni friends. Everyone ambitious and personable is in finance, law, medicine.
My 3 kids are all hardworking and sociable. The older 2 attend career events now as young teens and my son wants quant work experience as soon as he can.
The local state comp here has many v biright kids eg top set for maths is based on SAT score 113-120, where 110 os Greater Depth and 2 sets at this level (of 8).
Kids i know going private (£25k fees) are mostly only children, immigrant kids of builders etc sold a dream, mostly grandparent funded. One girl we know, funded by warehouse business parenfs, was below mid level for maths & english at school. One boy only child got a football sponsorhip but is not bright at all.
Also contextual scoring means private is seen more harshly.
I dont know, didnt seem a good investment of £800k, prefer to pay them through uni and have btl they can live in, instead. And pay for 4-5h turoring a week each child.
Good luck whatever u decide- but use pension calculator first :)