I agree.
I don’ t think fees will rise as much as people are expecting (and some of the rise will come from inflation, in any case). Private schools are already getting ready to trim costs and get round the change in status in various ways. And I have heard that if schools lose charitable status, they will be in a position to raise revenue more in other ways; I mean, if you are no longer feeling the need to share your facilities with the local state schools, for example, you’re now in a position to use those facilities in a way that raises revenue. Private schools are also going gangbusters on overseas branches in middle income countries and East Asia. Those will bring in a lot of money.
There will be some movement into state schools, but probably less than expected, and more at younger age groups, where the numbers of young kids are falling anyway. I do think that good state 6th forms will see a bit of pressure, though!
The numbers I have been being run on this, suggest that overall, these changes will result in a net increase in funding for state schools, though not by eye popping amounts. (The sources saying otherwise tend to be from, shall we say, “interested parties” like independent schools’ organizations, which tend to provoke responses of the Mandy Rice Davies variety: “Well, they would say that, wouldn’t they?”)
I doubt that this will have any transformative effects on state schools. The idea that having private school parents in the state sector will put pressure on the edu sector to improve schools is nice, but I’m not sure it will work that way. These parents will mostly get their kids into good state schools that are already perfectly good, and not the troubled schools which represent the long tail of underachievement. Involved PTAs can raise money for sensory herb gardens or posher play equipment or whatever, but they can’t do things like “fund special schooling for those who need it so that lessons are less disrupted,” which might actually make a difference to kids’ outcomes. And former private school parents might campaign for higher taxes so that their local state school can be improved, but frankly I think they are more likely to want to keep their money and use it to have their kids tutored.