The reason airports don't do more for passengers is because they don't have any competitive reason to. No one is going to choose where to live, or where to travel, based on the quality of services offered at the airport. Flight schedule, perhaps, but no one ever said "let's live in X because their airport has more amenities".
In cities with multiple airports, they are usually run by the same authority and therefore do not need to compete with each other either. Los Angeles is one of the few places where several airports in close proximity are run by different agencies, but they don't have to worry about weather.
Interestingly, airports that are losing traffic to neighboring airports often come up with some sort of passenger retention mechanism. CVG had a rewards scheme a few years ago to stem the loss of passengers to DAY and CMH, I'm not sure if they still do.