Understood, @JHS. I suspect this probably comes down to specific school districts and specific private schools. I grew up in a very blue-collar district (today with +0.1 grades ahead rating in that NY Times survey) and now live in a more affluent section of a more middle-class one, but neither is remotely competitive academically with Lower Merion (+2.7) or Radnor (+2.9)–the “top districts” in this area (especially with regard to per pupil spending!).
Also, not all private schools are located in posh towns on the Main Line. There are some smaller gems out there that value more than superficial forms of diversity. Greater Philadelphia has an incredible range of private schools, unlike most areas of the country, and many offer generous financial aid.
I have no idea where the OP lives in CA and whether or not he has any non-public options along those same lines. A magnet school might be a great alternative, but I suspect it’s not an option. So (to bring this back to the original topic), if he has to go into hock for a private school, that just seems crazy to me, given that he’s in a good district and his son is doing well there. Especially if the only goal is to get into a top 10 or 20 university. I suspect he lives in a “Lower Merion” district, in which case, I agree with your assessment wholeheartedly.