I've parked in various hotels around where I live and there are different methodologies: everyone paid for parking; no one paid for parking; only overnight guests paid for parking and day guests had to park in an open visitor lot (which can't have overnight cars). And that's in the same city. It may or may not be related to size of parking lot, location/proximity to downtown, location/proximity to other amenities which have paid parking, general corporate policy, or other. I think that the only generality that I can come up with is that there is no generality when it comes to parking. And I can tell you that I don't live in anything I would consider to be a big city.
I work in a university building and pay monthly for parking. My parking lot is huge, is probably 10% filled due to our slightly remote location from the main campus and the partially empty building I'm in, and I got ticketed last week because I parked a rental car in it for 3 hours and forgot to put my regular parking pass in or pay for a daily parking pass. Corporate policy, money-making plan, fairness with other people who have to pay, deterence to those who shouldn't park there, bureaucracy...??... Regardless of where you are, any or all of these can be the rationale. It may not have anything to do with space available, size of city or proximity to a crowded downtown.
I think that one of the original reasons for providing "free" transportation and luggage handling from the airport was to encourage guests not to rent a car (i.e., you are stuck on-site and eating and spending money over and above your room rental fees). So there may not be a stated you-may-not-use-as-simply-a-luggage-service policy, but it kind of defeats the purpose from their point of view if you are able to spend money elsewhere. I rather suspect that they see it as spending money to make money and less as a guest courtesy service to be used as you please.