Not having a car in SF is great if you live near the Market St. tunnel and need to get somewhere on that stretch of the city. Otherwise it's pretty horrible. Sure there's buses and Muni Metro trains that will get you most places, but due to the layout of the city it will generally take you 3x longer to get somewhere via mass transit than driving. As long as this is the case people will keep their cars, even when there's horrible traffic.
That and in many cases Muni buses will be extremely late or bunched up. It's not rare to see Nextbus saying 30+ minutes and this during what are peak travel times. For me it's often faster to walk if the distance is less than 2 miles. This is not an option for a lot of people unfortunately.
Also, what do you do if you live in SF but regularly leave the city? Mass transit is OK for specific things, but Caltrain and BART can only get you so far. I work in Mountain View but will soon need to commute to Campbell a day or two a week. To take mass transit I'd have to take multiple Muni buses or trains or take one and walk a mile, take Caltrain, and then get on VTA somewhere in South Bay. At best my commute will be 2 hours one way and if there's any hiccup and I miss the 5 minute transfer window between Caltrain and VTA it's closer to 2 1/2 to 3 hours. When I can drive down 280 in an hour or so this becomes unacceptable as much as I would prefer to be on a train.
As long as the transit options in the Bay Area are as poor as they are cars will be a necessity for many people. SF would be awesome without them but I just don't see it as feasible. Makes me envy everyone I know who lives in London and NYC.
If we had transit like NYC or London then I'd be all about getting rid of cars.