I've never been to California, but used to live next to NYC. Could you expand on how the transit is 'classist' ? Is it too expensive? Does it not stop at places other than the suburbs?
In SF, the buses are dirty and filled with homeless and mentally ill people. Taking a bus home late at night is the plight of the commoners, the poorest class that work in the service industry and can't afford an Uber or taxi. And this class divide is why a BART strike is possible. The worst affected were those who didn't have a car too fall back on, or who couldn't work from home for a few days.
If something so critical as the NYC Subway stops functioning for more than a few hours, the MTA provides alternative buses and advance notice. A multi-day complete system outage would impact everyone, not just the poorest people unfortunate enough not to have other options.
So you're a minimum waged fry-cook or whatever in SF, you've blown 1/8th of your workday earnings just getting to-from work. You can get the monthly pass ($76.00/mo), but that's a bitter pill to swallow on those wages.
Oh, and you might not be able to take it home anyways since it shuts down at midnight, so don't get a job that does dinner service. Also, IIR, bus transfers to the Muni aren't free.
In the meanwhile the highly paid dotcommers might even get free company shuttles with wifi.
By comparison, a round trip Subway ride in NYC is what, $5? Goes pretty much everywhere, with good service even into lower income areas, transfers to buses are free. So while minimum wage is lower in NYC, it doesn't even kill 1/8th of your workday's pay to get from home to work and back.
Because coverage is so good, it's also unlikely that you'll even need a car, so you can save on all that expense: gas, taxes, registration, insurance, etc.
If you can bike (which I do), though, the calculus quickly changes.
I was astounded when I visited SF, usually seen as much more bike friendly than NY, and I saw that east bay riders still had to rely on the BART to get them into the city. The fare between West Oakland and Embarcadero alone is more than a subway ride.