There's a very large population of bicyclists in Tokyo. Keep in mind for people living in the city, the bicycle is a utility, not something ridden for sport or enjoyment. I do however enjoy passing cars on the bicycle and instigating races from bicycle road racers during my commute.
Your second sentence contradicts your first. How do you encounter road racers if the bicycle is "not something ridden for sport or enjoyment".
I live in a city and it is all three for me. All my trips to the grocery store are on bike, but I also enjoy the occasional leisurely ride to nowhere, and a regular "sport" ride.
But I do agree that most people don't think of a bike as a tool, they think of it as a toy. I think of cars like that, though, so I guess it is just a matter of perspective and experience.
Road racers are a very small minority of the cycling population in Tokyo. However, almost everyone (non road racers) rides on the sidewalk. On the street there are relatively more road racers and hybrids.
It probably works pretty well, since there's similar car-parking technology (exception: see jac_no_k's experience).
But I'm reminded of France's expensive investment in public bicycle rentals ($3500 each!!) which is not going perfectly: http://www.treehugger.com/files/2009/11/velib-bike-sharing-t...