Market st is already a no-go for private cars for many blocks. As much as I hate the scooters that go around in the sidewalks and then park haphazardly blocking the path for disabled people, they did reduce the traffic around Bart stations quite a bit. If it's easy to use the alternative, people do take it. There are a few who'd never leave their precious cars but most others care about the commute and not necessarily the mode.
Every metro region in the country must be a unified under a single transportation agency. They should have enough power to force major changes. If transportation is designed at one level above a single city (esp in a metro area), there could be a lot of efficiencies that can be derived. E.g, coordination between bus and the subway system to pick up passengers within a few minutes of disembarking from the train. Expanded subway coverage for arterial routes at least. Mini buses instead of big ones for feeder routes - with increased frequency. This is not uncommon outside the US btw.
Next up is zoning changes. Local groceries must be encouraged. There should be space kept aside every few blocks and it shouldn't be just a liquor shop - there should be explicit guarantees on providing basic amenities and produce. Small scale restaurants must be allowed in all areas. This reduces the need to go too far for regular shopping.
Then, increase gas tax - don't tie it to gas price. Calculate based on the needs of costs of highway maintenance and public transportation needs. Use that to provide subsidies for public transport.