I think your theory that competition in public transit can lead to better
service has to overcome a great burden of history against it.
Think about the history of public transit in this country in the 20th
century. I can't think of any situation where the ability of a private (or
sometimes public) provider to skim high value routes or passengers has not
been a major feature of contraction in service.
It is worth remembering that competition is a destructive, not a
constructive force. (Really, think about it.) This doesn't mean you don't
sometimes want to harness the destructive force to achieve useful social
goals. But I would suggest that it is a force to be used carefully. Yes
it could be used to shake out some of the rigidities of SF's public
transportation. But no, it is not a creative force you can set going and
expect a positive outcome.