I don't consider a train that runs between a city and its airport a "train," to me it's a "shuttle." Like a subway, if you will.
Huh?
A shuttle to me is a small 8 seater van/bus that takes you to the nearby hotel from the airport.
Since the Narita Express is a limited express service, and shares tracks used by other local services, a schedule is important to maintain.
Keisei mainlines terminus just happens to be terminal 1 airport station, I wouldn't call the trains that run on this line a shuttle, even though yes they do run between a city and it's airport, as both the Skyliner and Limited Expresss do serve passengers who's origin,final destination may not be the Airport.
It would never occur to me to ask someone in Chicago or NYC for a "subway schedule." All you need to know is which platform to stand on, the trains come and go all day long every few minutes.
Yes, but subway/mass transit lines are a little different. Certainly if I'm at x street station and wanted to go to Penn Station on the NYC Subway all I need to know is what platform to stand on and trains will come by to take me there. But if I wanted to get off at Penn Station to catch the next Acela to Newark, then I would definately want to know the train schedule.
As mentioned even the subways and other mass transit systems that operate in Tokyo and other parts of Japan do operate on a schedule, and unless the ground under the tracks are falling or some delay happens, trains will usually stick to their schedule.