I'm not sure it's a good idea to take the BART strike and frame it as a small-scale example of the role of unions in the U.S.
The reason BART operators have so little support in S.F. is that they currently do little and get great rewards for it.
Of particular interest are the overtime policies. The operators can easily exploit the system to bring home over half their base pay in overtime. They are allowed to call in sick for their regular shift, then work an alternate shift for OT. Not surprisingly, attendance has become an issue as well.
If the rank-and-file want a raise to their base salary, exploits like this will have to be closed.