The ATC rep who spoke to our group said "We really prefer all traffic in our coverage area to be talking to us and on flight following".
There are the VFR Airways noted by the magenta arrows, that must receive clearance and remain in communication with ATC.
The VFR Flyways on the coast and east-west in the South Bay are outside Bravo and communication with ATC is not required. Radar coverage is spotty below 3500' along the coast, and ATC would rather see the traffic on radar and be on flight following.
VFR Flyways over the Bay, transition mid-span of the Dumbarton Bridge and have 2 branches to the north and 2 to the south. There's a requirement to be in contact with KOAK tower for Charlie clearance, and to expect mid-field transitions at 2000'. ATC said they prefer this traffic is on flight following for automatic data hand-off to KOAK tower, especially if transitioning through the area over Oakland.
He said outside (including under) Bravo, pilots can follow FAR's for contacting the authority governing the airspace, but they would rather be involve and help with the transitions.