The geology of the Bay Area would make that difficult. The Peninsula flats are mostly loosely-consolidated sediment, and in some areas you have less than half a mile between the mountains and the Bay. And it's less than 2 miles from the San Andreas fault. You'd likely have significant problems with flooding [1], and all the difficulties that the Pacheco Pass segment is having tunneling through an active fault would be multiplied by the 4x as long, geologically varied segment from SJ-SF.
[1] This is a significant issue for the NYC subway, even though you don't really think of NYC as being on top of a bay.
[1] This is a significant issue for the NYC subway, even though you don't really think of NYC as being on top of a bay.