You're comparing apples and oranges. In America, parking at the airport is absolutely normal, because it's a car-based culture and there's generally no public transit to the airport. There's enormous parking lots for cars at all airports there. The alternative is usually a very expensive cab ride, or trying to get a friend to drive you.

In Japan, parking at the train station isn't normal in the least; I don't think they even have a place to park there. The normal way is to take public transit there. Same goes for the airports (at least in Tokyo); it's not normal to drive, it's normal to take the train, though some people take taxis because they have a lot of luggage and carrying heavy suitcases on the train is a pain.