I'm sure there are parents who assume private is always better than state and won't even look at local state options - but I suspect they are a minority of families. We looked at local state options (having assumed we would use the local state school), were quite surprised to find a load of issues there and uncertainty about school location/head teacher so looked at a nearby private school- which was much more impressive in terms of organisation, environment, feedback from other parents - so chose private. I think that's how most parents go- plus those leaving state as it's failed their kids.
Then there are people who are in an expensive city and can't afford a house in a good catchment area, but can afford private school fees.
I want my kids to have an excellent education. Why that is 'buying privilege' when somehow buying into an expensive school area or buying tutoring or an ADHD or autism assessment, or extracurricular activities isn't seen as 'privilege' I really don't understand.
My kids are privileged- given that they are from a middle class professional well paid family and so far have zero adverse experiences that's a pretty non-brainer comment.