The BART Transbay Tube and all the trains that traverse it during peak hours are fully saturated. Capacity can't expand until CBTC signaling ships in the 2030s. The Temporary Transbay Terminal bus bays are also fully saturated, and the buses that service them have little headroom. Saleforce Transit Center was supposed to pave the way for more Transbay bus capacity, but 10 years of construction bought us only a few weeks of service before structural failure.

In short: public transit alternatives to the Bay Bridge are already too popular. Shifting SF<->Oakland car trips to public transport is physically impossible in the short and medium terms. BART does not have space to accomodate the 270,000 daily Bay Bridge drivers, and there's a 0% chance of making that space in the next decade.