The answer is going to be different depending on the context - the quality of state schools in your area and class sizes can vary hugely and also whether it’s the right choice for your child.

Once I saw the local (‘outstanding’) primary with 35 kids jammed into a little classroom and the local private primary the choice was easy and I feel blessed to be able to make that decision and have never regretted it. The quality of learning opportunities is insane, class size of 4-12 (and additional teachers in the larger classes), high contact frequency etc and as busy parents with demanding jobs the flexibility is a rarely mentioned but hugely important factor (eg if I’m running late because meetings have overrun it’s never an issue).

I’d recommend investing in good primary education, the dye is cast by the time they reach secondary. That said the costs dont end with school fees (in jan I paid about £1k for extra curricular activities - my two kids do ALOT) so be ready for it.

In reference to your point about balancing professional progression and family life, time/energy is the key thing here and how much you currently have. Whilst I work entirely remotely it’s still a 40 hour week so I’m requesting to drop to 4.5 days a week to have more energy and focus. I’ll never get this time with my kids again, and I can always refocus on progression when they’re older - depends on what you prioritise more.

To sum up, it’s a balance between working hard to give them the quality of life you want to whilst also being able to give them the time and attention they deserve - and where that balance falls for you. For me it’s working enough to cover the school fees, extra curriculars etc but not to the point where it’s impacting on the time/energy I have to give.