So just to clarify, you're thinking that traffic would increase because people would live outside SF and commute in? But don't people who live in SF need to get to work too? In that case, it seems like having giant highways carving up the city is going to make walking / biking to work harder which would cause more people to drive to work. That's what we see in "car-oriented" cities and it leads to an increase in traffic congestion that makes it miserable to drive, in addition to an environment that makes it miserable to do anything else but drive.
Commute through, eg Mill Valley to South San Francisco, or similar. Right now, because there's no freeway that goes through the city, that commute is technically possible, I'm sure there are people that do that, but it's not a fun or easy commute, so people try and live in San Francisco and commute to one or the other. If there was a freeway from the Golden Gate bridge, through the city, instead of Lombard and then Gough, then the Mill Valley - South San Francisco commute would be (more) viable at a cost of increased inter-city traffic. Ie traffic that is in San Francisco, but not doing anything there other than transiting. Which is the so-called "extra" traffic GP refers to.
