We didn't educate our children privately, even though we could have done.
I think the idea of buying advantage for one's children is immoral and that all education should be properly funded to give every child the chance to fulfil their potential. If everyone is educated well then the whole of society wins.
I also did not wish my children to grow up in the bubble that so many children we know do. Their parents went to particular schools and universities, their children follow them and they all move in the same social circles. They have no experience of what life is like for people less fortunate than themselves and until these social barriers are removed, nothing will improve.