So, in this thought-experiment we start by travelling back in time 400 years. There are no state schools. Some, but not all, parishes have small schools to teach the children of the parish the basics of reading, writing and arithmetic, snd those are funded generally via donations to the churches that run those schools. It's a bit hit-and-miss. Wealthy families educate their children by employing a live-in-tutor but obviously not many can afford this
As a wealthy benefactor, possibly of nobility or royalty, I decide to create a school. I endow it with sufficient funds that 30 pupils from poor families can attend free of charge, and provide that additional places can be made available at-cost (ie no profit made) to such families that can afford to pay something for the education of their offspring but whose wealth is insufficient to employ a tutor etc - so merchants, farmers, general yeomanry free people of the "middle classes" whose aspirations for their children are for more than a little bit of literacy and numeracy.
It seems to me that this setup is clearly charitable and legitimately so. Education is ultimately a good thing and I am making it freely available to as many as I can afford to support, and available at no-profit for as many additional people as possible.
So - where did it go wrong? Fast forward 300ish years and at my school there are still 30 pupils getting their education for free, and hundreds more getting their education for "no profit" but the people paying for their education at-cost aren't the original "target audience", it's a much more privileged bunch. Was this a failure in my original foundation of the charity that I didn't make enough specifications to make sure the educational opportunities were targeted well?
At that point the State decides to start offering universal education funded through general taxation. My school has no obligation to be involved in this as it has been endowed as an independent charity with its own founding principles and it is not for the state to over-rule that - but should the state at that point have created more mechanisms for the better integration of these pre-existing charitable schools with the new state-funded provision. Where did the State sector go wrong that lead to such a huge gulf between the pre-existing schools and the state-funded schools?
There used to be some such integration. Lots of the old schools indeed were integrated for a while in what was called "direct grant" status where each independent school participating took some state-funded pupils as well as those paying their own way. (My dad went to one as a state funded pupil)
But Fast forward the last hundred years and all those efforts were disbanded. No more direct grants and no assistanted places.
It seems clear that the original foundation of these schools was clearly charitable and they have been operating under their founding principles to provide education for hundreds of years. It's also clear that there's a serious skew in who benefits from that charitable foundation and although there are still, 400 years later, 30 pupils getting it all for free, the "at cost" people are getting the "rolls-royce" version which is orders of magnitude more luxurious than the original founding benefactor ever intended.
Can any of this be rewound without smashing the principles of charity law that allow charitable bequests to perform good works? Can a fair version of charitably-funded education exist independently of state control?