No one in the UK pays directly for state education so your comment about private school parents not paying directly for it is an irrelevant point.
The point is private school parents could access state education which would cost ALL tax payers £8k annually for each child - and by not paying it they are saving the tax payers this money.
A child enters the education system for a number of years - anyone with a heart knows its not the best situation for a child to move schools if they are happy and flourishing there.
If Labour had of said all new private school joiners from now on will be charged VAT then that is a different story - parents could make an informed choice before starting in the system.
You have to remember that we are talking about a group of kids who experienced the disruption to their education and social development because of covid - its not just the SEN kids moved into private that are going to be badly affected by this - its also the kids moved into private because their schools did not keep up with their learning during covid. Kids that otherwise would have stayed in the state school system but their parents have stretched to private to plug covid gaps...and in doing so reduced the burden on the state school system.
Introduce VAT if you want but for fuck sake give this generation of kids affected by covid a break - they have had enough disruption to their education.