As somebody who cycled Market Street every day for a few years, I beg to differ. Private cars were always my biggest safety worry. Per the MTA, it was 200-400 cars per hour during morning commutes. That's half what's on Mission, but it was still plenty to contend with.
I cycled Market every day too. Far and away the scariest thing is a bus on my tail. Far and away the most frustrating thing is a bus in front of me. I switched to Howard because the trucks forcing me to weave in and out of the bike lane were less of a hassle. Excited that Market is eventually getting a dedicated bike lane as part of this project, though.