Granted this was 20 years ago, but I used to fly a fair amount out of the Bay Area. I don't remember ever catching a connecting flight at LAX. Usually it was one of Denver, Chicago, Salt Lake City, Atlanta[1] or Las Vegas.

One of the arguments I did read that was convincing is that Bay Area and LA basin airports are near capacity. Diverting passengers from the LA to Bay Area route would free up capacity for long distance flights. Thus alleviate the need to expand those airports. In the discussions I've had it's come up that expanding airports in built up areas is massively expensive. They want to add a third runway to Heathrow at a cost of £14 billion. That's 25% of the projected cost of CHSR.

[1] When you die, no matter if you go to heaven or hell you'll transfer through Atlanta.