All good suggestions Blackberrycream. I'd be happy to give up advantages, because, while my dcs might miss out on a top school place, it still seems a saner choice to want to live in a more egalitatian country where huge groups of people aren't sidelined.
Not sure why the existence of tutors would mean 'having it both ways'. The issue under discussion is private schools, not any other ways you want to spend your money, whether educational or not.
but not all private school teachers are eligible to be state school teachers
We could have a transition period of a few years where private school staff are still paid as teachers and will be supported to gain qualified status, maybe a new qualification, or give credits based on experience.
So Eton becomes a state school with fabulous sporting amenities with every sport catered for - rowing, fives, swimming, tennis, you name it, a state of the art theatre, recording facilities, fantastic music provision etc etc
This surely highlights the need for change, not the problem with change? It's obscene that all those facilities exist for 1300 boys, while 3 million state school pupils are lucky if their schools still have a playing field.
The biggest issue would be when these schools are not in highly populated areas. So not too much problem for Eton, Harrow, Westminster, etc as they could have large catchment areas and ballot for places. Those schools could turn into well resourced large comprehensives. Existing schools nearby might merge with the independents and move into the better resourced buildings.
Some of the facilities could be turned over for other public use or shared by several schools. You could also have state boarding facilities as mentioned in a pp. Some costs could be offset by renting out some facilities for extra curricular activities, as conference facilities, or to provide/replace public leisure facilities like libraries, theatres, sports pitches. They could house local authority music hubs, be used by universities, football club academies (which already have partnerships with state schools), etc. And some buildings could be sold or leased out if not needed for educational use.
For schools in rural locations where there would not be the population to support a state school, perhaps there are universities with poor facilities which would welcome a move to a new campus. And maybe the National Trust could create a museum to remind us of the segregated society we once lived in.
These are just a few ideas, off the top of my head. My point is that none of the objections I've seen so far are insurmountable barriers - they just need a bit of creative thinking.