In the end, this is a risky policy whose effects are simply too unclear. It will drop a bomb in the education sector and nobody really knows how big that bomb will be. It might be a tiny little firecracker that nobody notices much. It might be a great big bomb (at least in certain pockets of the UK).
But why do this now, when it's pretty obvious that it's not going to raise much revenue, and it's going to soak up a load of government attention, just at a time when the new government has a million other things to worry about?
Tony Blair understood the way to approach this. You completely ignore the private sector, and you accept that what you have to do is use general taxation (increased if necessary) in order to improve state education. You allow private school parents to carry on choosing to spend their money on saving you the cost of educating their children. You recognise and probably regret that this means that richer children are getting a better education - but you also recognise that if you want wealth creation (which Starmer says he does), then you have to allow the people who facilitate this wealth creation to spend their wealth on making their own lives better - otherwise they'll go elsewhere. So you let them carry on, while you use the wealth they're creating to make state schools better. In the long run, if you do this, then you will ultimately achieve a higher proportion of children in state schools, because parents will vote with their feet - if state schools are reliably good, then only the very richest will choose to pay to go private. And actually, nobody cares very much if some kids are still going private, as long as everyone is getting a decent education.
The problem is that KS has moved his party towards the centre in order to make it electable, but a lot of his members are not happy about being there. This policy is just one example of that. They still hold the Corbynist view that equality is what matters above all, at all costs, and that if the route to achieving greater equality is (in the medium term at least) to make things worse for those at the top rather than better for those at the bottom, then thats what they want to do - even if the 'equality' they ultimately achieve is actually worse for everyone in the end. It's the very definition of levelling down rather than up.
I'm not a Tory defender, not at all. They let the private school sector carry on without doing nearly enough to improve the state sector. But if KS is going to be a centrist than he has to actually act like one.