Here's a better idea: charge market rate for parking on the street, citywide. There's no reason that space should be given away for free. Use the revenue to build some much needed trains.
Roads are public goods and more importantly they are built with tax money. They are also specifically built for cars to use and without a place to stop they are a bit meaningless in a city. They might just change this and start charging but that's a pretty stupid idea. Free market is not an answer to everything.
Not to be too pedantic but ... the roads in SF were built long before the car was invented. Think about it, if SF were built _for_ cars, why would it be at the end of a peninsula so cars have to cross bridges to get to it? SF was built so that it was easy to access by sea from ships. Cars came much, much later and the issues with parking, etc... really stem from the city not being in a very good location vis a vis cars. I agree that roads are a public good but I think they should be used to provide the greatest economic benefit which, in my opinion, is not to get commuters into the city.