The state of San Francisco's transportation system, whether it's BART or MUNI, is a reflection of the city and its problems, not just of the transit system itself. I sincerely hope you noticed the homeless and mentally-ill that are everywhere in the city before you noticed the elevators they shit in.
Just like human shit clogging up and breaking down escalators (true story, I wish I jest), it is BART's problem, but BART and its employees are more or less powerless against it. When you have a veritable army of homeless and addicts inhabiting your city, there is not much you can do besides stay in that booth.
If you would like functional elevators that aren't biohazard zones, I'd suggest becoming involved locally and solving the problem at its root. I am confident you will get nowhere with clean elevators until you get somewhere with reducing the homeless and mentally-ill population.