And yet they do! Areas of social deprivation still have hospitals, law firms, universities, big industries requiring highly specialised skills etc - they employ people and pay them a salary that goes a long way in areas where housing/living costs tend to be low. Meanwhile, the local state schools here sit at the bottom of league tables for GCSE results.
We could all up and leave so the area doesn't have educated professionals manning important local services/industries. But, instead, some move further out to the nicer countryside, where they pay more for housing and get better state schools but have a lengthy commute. Others of us choose to live closer to where we work and pay for private education.
In a perfect world, the local state schools would improve (and to be fair the local state primaries are very good, it is 11+ where the problems arise). I hoped that would be the case by the time my DS got to 11. But, by that time, there had been no obvious improvement in the local state provision. They had become more limited in their resources and opportunities available, with even bigger class sizes. The private school was the only school in the area offering the options that I had been fortunate to have in a state school in another area of the country. So, it wasn't state vs private - it was which school offers what we want for our child. We're lucky enough to be able to make that choice because we earn the money to pay for it.