https://en.wikipedia.org/wiki/Upper_middle_class_in_the_Unit...
Commute times are a real factor in deciding where to live, and which schools to pick. In the Bay Area, the only real solution is living closer to work, which requires over bidding & selecting private schools if they picked the wrong area.
Almost everybody who is upper middle class in the US doesn’t live in San Fransisco, so find a better comparator.
Also $160k household can be very different in terms of childcare costs depending on how many people in that household are working, and is an actual problem for double income families with young kids in HCOL areas.