One reason many people are more concerned about inducing driving demand is that private vehicle travel generally emits more carbon, uses more valuable land (e.g. parking, highways), and results in more fatalities per person per mile than comparable forms of transportation.
Another problem with inducing driving demand is the degree to which those costs are subsidized by taxpayers (roads, highways), other shoppers (required/subsidized parking), or left as externalities (carbon, noise). Tolls, gas taxes, per-mile fees, and parking fees would have to be quite a bit higher in most places to cover those costs.
If induced demand is high enough even that, too, may not be enough - but then building a new rail line is at least no harder than adding a new highway lane (in most cases), and can support substantially more throughput with equal or lower travel times.
By the way, even BART could increase throughput today without adding more lines. Not all trains are 10-car trains, because they don't have enough cars in the fleet. Adding more cars to their trains is a significantly cheaper prospect than adding a new lane to the Bay Bridge (which was also basically fully maxed out on throughput during peak traffic times, pre-COVID). And BART carries substantially more people across the Bay than the Bay Bridge does.
So, certainly the BART needs more capacity, both now and in the future - but so do the highways.
Note that I didn't make my point to say that we should build another bridge, just the pedantic detail that BART traffic isn't that much larger than Bay Bridge + San Mateo Bridge, which is a more apt comparison. I think actually you'd want to add in the Golden Gate Bridge, another 110K. So basically, there are more people commuting into SF driving over bridges than taking BART in.
To increase the capacity of the red line would take a lot of work that would not be cheap. For instance, the length of the trains could be increased, but to do that you have to construct new stations, since the train is already the length of the entire platform, at least the ones used for rush hour. LA has actually lengthened platforms that are on the surface before to accomodate longer light rail trains, but underground this is so much more difficult.
You could lower headways from the 10 minutes they are currently at, but this becomes a physics problem fast. One issue is a lack of turnback stations at the ends of the line so the train has to come to a stop then 'reverse' at the end. Another issue is a subway with a train works like a pneumatic tube, there is a volume of air moving that needs sufficient ventilation, which is why you see these big ventilation grates on sidewalks where subways run below, and to run more frequent trains would require significant upgrades to the ventilation systems along the entire line.
Of course, you need to invest in the infrastructure to make it work, but it's very possible.
A quick Google suggests that in Tokyo they even hit 50 trains per hour, so one every 1m20s, which is insanely impressive.
Mostly DC metro rail and a bit of LA buses, FWIW.
Lots of places talk about the importance of walkability and mass transit but if you actually look at most transportation budgets the vast majority goes to automobile infrastructure. Even what passes for "pedestrian infrastructure" in many places is there for the benefit of drivers[1]. I mean, it makes sense because everyone in the US drives everywhere, but it's a chicken-and-egg problem.
[1] https://www.strongtowns.org/journal/2021/1/29/pedestrian-inf...
Of course, there are also other potential advantages of public transit unrelated to induced demand, like pollution, safety, cost, impact on the design of living spaces, etc.
It’s just inducing demand on an already overused system like private cars doesn’t fix the system being overused unless you can get beyond the desired capacity.