Actually, it is possible. There is a free shuttle that goes from UCSF to the BART station and back again. You can read on the shuttle and on BART so it's not really wasted time. I think the shuttle runs until after midnight so its possible to stay late for electives or late studying and still get back home at the end of the day. It does cost a few bucks to ride BART, but if you have cheaper rent and you are settled into your space it is probably a wash. Driving from the East Bay, however, would suck.
I live in Pacifica and drive to school every day. Yes, it is possible to find free parking. I do have a bit of a walk and I count that as a plus since it means a little extra exercise. I also like being totally away from school at the end of the day from a mental health standpoint.