A simple way to understand why local governments shouldn’t underprice parking, is to think about what would happen if local governments were in charge of setting gas prices.
Everybody likes low gas prices and not high gas prices, so a $2 price ceiling for gas would enjoy lots of political support. And it would totally work -the price of gas definitely would not go above $2.
So why don’t any politicians propose capping gas prices? Because everybody knows that price caps would lead to gas shortages and long lines at the pump.
It’s the same with parking. When the demand for parking spaces peaks, and the meter price can’t go higher, you get long lines (traffic congestion) as people circle round and round looking for spaces. Here is a fascinating paper from Donald Shoup looking at the relationship between traffic congestion and parking prices.
This ought to be pretty intuitive, but for some reason parking is an issue where many usually-sensible people have developed very strange views on the economics, or want to dismiss insights from economics in favor of “cultural” arguments. In reality, there’s a rich literature studying behavioral responses to parking price changes in many different kinds of cities and the effect is the same – higher turnover and greater convenience finding spaces.
The position that’s totally lacking any empirical support is the notion that low prices mean more customers for downtown businesses.