The problem with SFO is not fog, per se. It is the fact that the runway pairs were built with substandard separation )the 10-28 pair is built on a narrow landfill extension pier) which requires one of each runway pair be closed when there's any impediment to visibility (rain, not just fog, and rarely smog) and any other FAA mandated conditions that might call for traffic reduction and separation.

OAK would often be a preferred choice for that reason, and the OP indicates greater convenience for access reasons as well.

WN / Southwest seems to be the only airline flying BUR-OAK nonstop.