Having lived there in the early 90s, I can say that my car was much more of a hindrance than a blessing!
I moved here three weeks ago and I'm selling the car I have back home ASAP. You're exactly right: transit is so plentiful and cheap, and walking so easy, that I have absolutely no desire to register, insure, drive, and park a car here. It's way more of a hassle than just taking the BART or Muni to within a block of my destination and walking the rest.
I hadn't been on public transportation in nearly two decades before moving here and was never interested in it, but this has won me over. It's a model of how it can and should be. Plus, we have Zipcar for when you really need to drive around for a few hours.