To me it’d depend on the local private schools, and how good the state schools are - or not.
There are plenty of mediocre private schools, so from an academic POV, a good state may be better, at senior level anyway.
Fees are a lot more relatively expensive than they were a few decades ago, so coupled with the increased cost of housing, a lot of the sort of parents who would have been able to afford the fees, can now no longer do so. Our dds attended a highly selective senior private school, but very few of their old schoolfriends with children are now paying fees, and those who are, are mostly having help from grandparents.
A school some relatives’ dcs attended, which was selective and regularly reached a very respectable point in the league tables, has now dropped right down. I am told that this is because their admission criteria have had to drop, so they’re more or less taking anyone who can afford the fees.
According to the relatives in question, a good percentage of the pupils are now spoilt rich kids with not necessarily too much between the ears. That is now certainly not the sort of school I’d have wanted for ours.
I dare say a number of private schools have gone the same way.
Presumably the sort of private schools that were always very selective academically, and therefore sought after, particularly in densely populated areas, will have less trouble attracting bright pupils.