Parking is the 'egress' cost of visiting a place. Like a transit system where you pay on exit.
People seem to find paying at the end of a journey more acceptable. Perhaps because once you've made the journey to a place, there is already a sunk cost to the trip, so you are willing to pay more.
What if we did transit fares this way? No standard fare, just a location-specific egress cost. (And if they want egress costs lowered, local merchant associations can chip in a subsidy).