No, the idea is that storing cars takes up a lot of public space. Each parking space is basically a tiny garage.

Why do we give away garage space for free to car owners? Storage for your vehicle in a busy city shouldn't be subsided by default. The space is too valuable and could be used instead for better public benefit.

Sure, at the same rate as cars, $20/hr per 12.5m^2. Since I take up about .25m^2, my bill for today ought to be about $0.10, so let me know how I should pay it.

Or we can acknowledge the reason we have money: to distribute scare resources. Parking in urban areas is scarce and expensive, while space to walk and sit simply isn't.