You have simplified beyond the point of meaning and right into falsehood.

1. Education isn’t just taxless, it’s completely free. 100% subsidised. No one needs to pay anything.
2. You’ve confused education in general (good) with private education in institutions whose whole purpose, bar none, is to give the children of wealthy parents an advantage (bad) over the children of non wealthy parents.
3. Private schools also (bad) insulate wealthy children from non-wealthy children so they never know anyone whose getting evicteed by a scummy landlord who just wants to get rid of them because they complained about the mold. They never know anyone whose patents have to scrape by with universal credit and they never develop any sense of just how badly ordinary people struggle financially or how cruel and harsh is the world of “I’m sorry, but the country can’t afford to give you money for the wheelchair as well as the false limb.”
4. The PTAs of schools with wealthy parents tend to raise plenty of money for equipment. Patents with a spare thirty grand or three knocking about for education stops benefit society far more if it were state schools being supported.
5. Good therefore tax free has no basis in logic and if the chancellor made everything good tax free, she would shut down the government.

You keep bringing up wealth tax as if it’s either this or that. It isn’t. I’ve not seen anyone here argue with taxing wealth. Do both.

Tax unnecessary inequality-perpetuating private education like every other luxury and tax wealth too. Both. Simple.