The link you provided overlooked the key fact that SF has another system that's far more like SF's version of DC's Metrorail: MUNI -- even though the MUNI cars and payment-mechanism doesn't look as much like Metrorail as BART does.
The idea of extending BART to provide more central-city service isn't even considered, because the BART system was created primarily to serve regional, long-haul, city-to-city needs. BART is the LIRR or PATH trains, not the MTA subways, of the bay area.
The internal SF system at the dense core is being extended -- a controversial new 'Central Subway' from Chinatown to CalTrain/SOMA -- and it will be part of MUNI, not BART.
And you pointing out that the California state government isn't high-functioning? Well, that's just mean. Fortunately, as an authentic Tex-Yorker, I have a tough skin and am not particularly sensitive to such slights.
Why? Well, if you go north of the BART line you're rapidly into the hills, so either you have to take the trains up the grade (bad idea) or you have to build your stations thirty storeys underground (also a bad idea). If you go past the hills and up to the Marina, you're into reclaimed land so I don't think it's possible to build a tunnel (civil engineers out there to comment?)
You could probably extend it out into the Richmond and Sunset districts, but that part of town is served reasonably by buses anyway.
While I hate to defend BART almost as much as I hate to ride on BART, its main purpose is really all about linking the cities of the East Bay with San Francisco, and San Francisco with the airport. Comparing it to a proper metro system in a city not subject to the weird geographical limitations imposed by the hills and the Bay isn't really fair.
And I'm sorry you bring up his city of residence. As a Texas-born New Yorker, I'm particularly sensitive to this fallacious ad hominem. Or should I discounting your arguments because you're presumably Californian and your government isn't particularly high-functioning?