But that doesn't resolve the question of the supply of parking spaces - i.e., how many there should be. That only allocates the existing ones.
Also, it allocates them to those who can pay more; that's not always desirable. For example, should citizens' access to the grocery store be limited by their ability to pay for parking? To city hall?
I don't own a car because it doesn't make financial sense for me to do so. That's the kind of longer term market impact you'd want to see.
Edit: The choices are not between allowing people to go to the grocery store and courthouse or not, it's between taking the bus and driving. I do just fine on public transport without a car.
Realtime bidding would be a UX nightmare, though I guess it's Econ 101 (i.e., ignoring lots of real factors, including transaction costs) optimal.
Rather, I think a municipality setting prices by fiat to be something that mostly gives the an approximate solution most of the time.