Many of those prep school families would tour good state schools as a 'back ups, to back ups, we did it for state primaries too, knowing we were set on the private school that DC attends now.
I agree with you though the CoL crisis has persuaded some families to switch from private schools, its going to be hard to measure until next year.
The CoL , I've felt it in food prices and higher fuel bills, but it hasn't really made a big impact on my family YET if I'm honest, we switched to variable direct debit for energy as my energy company were taking the P with their estimated bills, and put our boiler down a notch , and our heating bills aren't too bad, YET. Our mortgage was locked for 5 years at a tiny rate last year, so interest rates don't impact us. YET. Job market (in our fields) looks steady, may change so a big YET on that too.
The CoL , its impact on people with food banks, heat banks, it makes me think surely it makes more sense to send DC to a good state school and save our money. 30K sees you a long way in a year at Uni for example. My gut tells me everything will get a lot more worse before it becomes better , its the boom and bust nature of a market led economy.