I think that it sounds like a great idea considering that the cost of such system are a fraction of the cost of any public transportation. If one think of the cities that have a great public transportation system (like: London, Paris, New York, etc.) these are generally really costly and it is unlikely that a city would spent so much on them nowadays. I read that in Southwestern USA, Ford has had historically an active role in sabotaging the public transportation system to promote the car industry (and sadly they managed pretty well
). Also it seems like such system would accommodate with the individualism claimed by some opponent of the public transportation system. True, you won't smell the flowers anymore but then again, you would be protected from the rain and snow.
I just think that in most places, the number of cyclist is far from enough to create enough interest for this. Perhaps in places like parts of China, where bicycles are really used by a very large % of the population such system would take off. As I remember, there was a great (although limited) subway system built in Cairo. The subway was made by French engineers (in fact the tickets used are the same as that of the French subway) only nobody could afford it. Egypt never managed to completely paid the French for it and few locals use it because tickets are too expensive.