One thing state governments can do is restrain a local government's authority to impose minimum off-street parking requirements. Off-street parking requirements drive up the cost of development and encourage driving, traffic and pollution, but are often imposed in an attempt to create conditions where people can easily park on streets for free or to create conditions where commercial parking demand does not encroach into residential areas. Local parking requirements often exceed what is necessary to accomplish even those objectives.
For example, a state could pass a law saying "No local government shall require an amount of automobile off-street parking for a detached house exceeding two spaces." This would make a local ordinance requiring three parking spaces per detached house invalid and unenforceable.
Where this could really get significant is with multifamily housing like bungalow courts, apartments and townhomes. It's a common practice in many jurisdications, particularly in the suburbs, to require two or more spaces for even small multifamily housing units. This makes it hard to build the most affordable type of housing and results in some absurd situations like one-person households or zero-car households having two parking spaces. This results in what Donald Shoup called free housing for cars and expensive housing for people.
A state could pass a law saying "No local government shall require an amount of automobile off-street parking for a efficiency unit exceeding one space per unit." An efficiency unit is a housing unit intended for a single person, with zero bedrooms, where all of the living space is in a single room, except for the bathroom. These units are sometimes called studio apartments. This would make a local ordinance requiring two parking spaces per efficiency unit invalid and unenforceable. This would make it more feasible to build apartments and help to tackle the housing crisis in our expensive metro areas. Remember, a developer could still choose to build more than the minimum amount of parking if he/she thought it were necessary, but would not be forced to do so.
One potential downside to maximum minimum parking requirements is that a recalcitrant local government might attempt to down-zone land to avoid the risk of spillover parking. This could take the form of something like reducing the areas where multifamily housing is allowed by zoning more land to allow single-family housing only. Hence, the policy of capping local minimum off-street parking requirements would make the most sense in places like California where there are other laws in place to prevent a net loss in residential density.
Call it local control, within reasonable limits.