I think you're arguing for more grammar schools and for greater freedom for parents to top up their schools' funds, not for a tax on private sector investment in education. Neither of those two policies are remotely near Labour's agenda, quite the opposite.
If it was "look, we tax private schools and we're going to open a grammar school in every town" then we'd be having a different debate.
In that context, I'm always hearing "forcing private school parents into state schools will magickly make the latter improve". I'm always asking for evidence or explanation. I'm always noting that wealthy parents in state schools buy catchment areas and tutoring, then LOL when their kids are treated as "less-privileged" at Oxbridge....and asking why anyone expects departing private school parents to become massive advocates of the state system more generally, in ways actual state school parents are not.
Answers on a postcard, because until there's an answer, this thing is a myth.