Hospitals almost always charge because it’s usually near public transport and they don’t want people using their parking and using the train leaving nothing for the people that would need them. If they aren’t near public transport or a neighborhood (which is not a great place…) they usually don’t need to since it’s not being stolen by residents of the neighborhood or publicly tranport users.
If your gonna pay for parking, you mind as well pay to use the library and train too. Mind as well have everything paid and nothing is free with taxes. That’s what your saying here. That’s obviously a terrible way to do things.
In the ideal world, the parking and the amenities would both all be free. There’s no need or reason to charge for parking, other than pocketing the money, provided enough parking is available for everyone.