Yes there is - the city government that controls the parking spaces, also controls the transit system.
And again, it's far more realistic than hoping that a transit authority is going to find a buried treasure chest to invest in infrastructure while the public is investing more and more into cars.
If you want a real solution, provide tax incentives for companies to work remotely. If you eliminate commuters in those types of jobs that can work remotely, you solve almost all traffic problems.
Does an insurance salesman really need to travel to an office? 90% of that work is on the phone already and the other 10% could be replaced with video conferencing. I don't need to touch my salesman, I just need to hear what he's saying and read contracts. Unless your job involves handling physical objects, there is zero reason for a commute.
If you buy something that can't be carried, like a refrigerator, well, then you get it delivered.
Carsharing. Or a delivery service, which some supermarkets now offer already.
I'm well aware that other people need cars, but I'm concerned that there is one group of people that get the benefits of cars (people enjoying the calmness of their suburb which then commute into the city for work) and another group of people which gets all the costs dumped on them (people living in cities who have to live with the noise and air pollution and missing space for pedestrians).
In which reality do you live, wherein cars are totally fine?
This is debatable. In some countries there is an old tax for all car owners. They take the money specifically "for your right to have a parking spot for your car". But after you pay the tax, surprise, you realize that there is not a single remaining place with free parking in the entire city... by design. So of course, you are obliged to pay again. The car owner is taxed two times for the same service. Cling, mo' fresh money.
The planned scarcity of park spots is also a source of power and a weapon of mass destruction of high quality employments. If you restrict the access and monopolize the park spots, you can force easily the small bussiness in this areas to flee and make the whole neighborhood into recession. A handful of big bussiness that can build its own private parkings (or, even better, are strong enough to convince the local government to build a big parking for them) will quickly take all.
With the car problem, no one entity has the power to devise nor enforce a holistic solution. Of course, with the exception of a fascist overthrow of the state that tears down cities and rebuilds with central planning. The government can't just come and take people's cars away – you have a right to own a car (more or less). You don't, however, have a right to a parking spot, and it takes just a small city committee meeting to affect change.
That's not to say people won't get hurt by this, but it needs to happen for the good of everyone. Suburbia is bad for the earth and everyone on it. We need to start making some tough decisions... 30 years ago.