Nothing's stopping you from charging for street parking. If it's a subsidy, that's a political decision, not an inherent flaw in street parking.
Charging for street parking is a good step, but American neighborhoods still don’t have great transit and most people still have cars even if they are living in a house/apartment without parking. We aren’t like Japan where car owners have to prove that they have ample parking for their cars.
I believe Stroup showed a long time ago that the best solution is to price parking so that there is an average of one empty parking spot per block.