It’s so much more complicated than the simple choice you’re presenting.
My dc are all at private school.
Eldest is at an independent SN school. State options were not deemed suitable, both by us, and eventually (after a lot of expense and stalling) by the LA authority too.
The younger 2 are both at mainstream private schools, but are also both disabled. The private schools offer some advantages which help them (class size, for one) and some which help me (the wrap around care options, especially during primary years, meant no worries or clashes with end of school timings - eldest’s school is out of county).
My eldest won’t be in a position to have children, due to severe disability. The younger two may or may not be in a position in their futures lives to put any potential children through private school. Who knows.
Eldest will always require care, so house deposit not necessary (or not straightforward, anyway).
There is so much more to this than school fees = £250k, much better to save it and give to them as a house deposit.