I've used limo services a lot (they're really just a bit more expensive than using a cab really), and I tend to forget to arrange it before I jump on the plane. It has never been a problem to call a few limo services to ask if they have available limos to my destination and I've always gotten them promptly. In comparison, if you do pay per view for example, and the event/show is due in 5 minutes, is it not prearranged?

Let's use your example. On demand would be you stopping a taxi by waving like a madman on the street. That's immediate. UberCab is like me calling a Limo service (which is my example above) asking for a limo to pick me up at the airport and the limo arriving in 10 minutes. Hell I once called from the airport and a flight a different customer was in was delayed by 3 hours, so they gave me his limo sedan. I literally had on demand service, since I didn't have to wait for the limo to get there. I've done this in multiple states and it has never been a problem.