Main said..
No
The fees in private schools would double and people would leave them in their droves.
The state schools would be overflowing and the private schools would be half empty.
How could the state schools be overflowing? With all that money coming in, they would expand and perhaps get bigger locations. With bigger local schools you get more teachers and more subjects, and more economies of scale.
They don't just start gold plating the toilet cubicles. They build bigger schools, get demountables in as a temporary measure, employ more teachers, get a better range of subjects.
As a net result, the quality of teaching available in state schools would get better. There would still be crap teachers and crap students, but these would be at the lower level, so anyone striving for results is not going to see them.
Is it a bad thing if people leave private schools in droves? Why? Why should anyone care if they are half empty? FWIW you can't really have both. If the private schools are increasing their fees, AND are half empty, they will either reduce their fees to what the market will pay, or they will reduce their size. (They even teach Economics in State schools!)
From what I see, people go there because they are scared of state schools and see no alternative. If the state schools get better funding, then they will be better.