BART's incompatible Indian broad gauge does not need and should not get a second tube. Any second tube should be standard gauge. This was figured out a long, long time ago. BART is basically a money pit: pay 5 times as much as you would for a standard-gauge train and get less. Run electrified high-frequency Caltrain through the second tube, you get more benefits than running BART through it.
(Actually, BART should be standard-gauged, but nobody wants to shut it down long enough to do so.)
Your suggested plan is so ridiculous and impractical that I can't even think where to start. Anyway...
BART has invested in purchasing 1,081 new train cars to serve for the next 30 years. If BART is a money pit, abandoning all of that in favor of standard gauge trains is NOT a money pit?
Let's assume somehow one builds a standard gauge transbay tube and run electrified Caltrain through it, but then what? There is ZERO miles of electrified tracks in the east bay, so where does this hypothetical electrified Caltrain go after it comes out of the tube? Build an entire new network of electrified standard gauge tracks in East Bay? That will NOT be a money pit somehow?
What benefit would you even get out of it if somehow you managed to find real estate to construct new standard gauge electrified lines parallel to BART routes? If you suggest that BART itself should be made standard gauge, do you realize BART cars are single level and tunnels all over its network are built to that height? So how do you run double-deck electrified Caltrain over it without rebuilding everything? That will NOT be a money pit?
You know why does nobody want to shut down BART long enough to convert it to standard gauge? Because four hundred and fifty thousand commuters rely on BART every single day to get to work. What are all of them supposed to do for years while rebuilding happens?
Seriously... think a bit before coming up with ridiculous couch-expert ideas.