Well I would as would everyone else I know who uses private schools.
If VAT becomes the tipping point that makes you move to state schools then you were clearly at a point where you were maximising income. This might be through working more hours or for the second parent to be working to fund the fees.
If fees are no longer needed the major wage earner will likely reduce to 4 days, make bigger pension contributions or retire earlier much like senior medics who already do the same to avoid 60% cliff edge tax rates. No point working extra and paying a punitive marginal tax rate if you no longer have a pressing need for the extra cash.
A lot of people find fees through the second parent working FT. This is often the woman who then invariably struggles with childcare particularly in school holidays. No point continuing that struggle if the need for the money no longer exists.
All of these scenarios drastically reduce the tax paid and pass a further burden to the taxpayer that Labour are currently ignoring.
Ridiculously their forecasts are based on people continuing to work the same and spending what was the fee money on other goods and services that also attract VAT. That will never happen.