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.
(The part of BART that extends through the Peninsula runs aboveground from Daly City to Millbrae. For that matter, the part of BART that runs through the East Bay goes along the former Western Pacific right-of-way, aboveground. And the Transbay Tube was constructed with the "immersed tube" technique, built on land, towed out to sea, and submerged. Where BART runs underground and was built with TBMs, it's usually in bedrock under the cities of SF and Oakland.)
I mean, the Seikan tunnel was pretty difficult too:
> Following several decades of planning and construction, the tunnel opened on 13 March 1988.
> The construction cost of the tunnel itself was 538.4 billion yen at the planning stage, but it actually cost 745.5 billion yen. The construction cost of the strait line, including the attachment line, was 689 billion yen at the planning stage, but ended up costing 900 billion yen. During the construction, 34 workers were killed in the Seikan Tunnel, mostly in transportation accidents
> In addition, the tunnel faced criticism for its high maintenance costs, the need to pump a large amount of spring water even after completion, and that the large investment to build it is regarded as a sunk cost, and it is said that it is more economical to abandon it. It was ridiculed variously as "Showa's Three Idiots Assessment", "useless long things", and "quagmire tunnel".
We're complaining about CAHSR being decades in the making and billions over budget, but this does not seem to be unique to CAHSR. At least nobody's died during construction yet.
It's good evidence that all civil engineering projects are failures right up until they're done and everybody uses them, and then they just become critical infrastructure.
[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.