I live in Tokyo. People generally ride bikes on the sidewalks, unless they're riding on the really narrow side roads that have virtually no car traffic. The big roads do have painted bike lanes, but you don't see them used much, definitely not by the mothers riding mamachari; they're all on the sidewalks almost hitting pedestrians. Also, things are really different in different parts of the city. Some parts are newer with much wider sidewalks (and even dedicated bike lanes separate from the road), other parts are not. Some parts are just terrible for cycling, because there's too many pedestrians and the roads are hazardous (like Shinjuku).

The place would be a lot better for cycling if they installed more dedicated infrastructure, but it works as-is for many reasons: there aren't that many cars in most places, because parking is rare and expensive, vehicle speeds are rather low, motorized vehicles have most of the liability for accidents with pedestrians or cars (no matter what: if a kid runs out in front of you and you kill him, it's your fault), theft is very rare, and people are extremely non-confrontational so even though many pedestrians hate sharing the sidewalks with cyclists, they just put up with it. Back in the US, I had people screaming at me and trying to start physical fights with me when I rode on sidewalks and there was no one else on the sidewalk except them. Here, people just step aside. Another thing here: cyclists are legally required to carry liability insurance, in case they hit a pedestrian.

Anyway, you're not going to replicate Tokyo's success with cycling by simply copying one feature. The whole culture here makes it workable despite the lack of great cycling infrastructure, as well as many other things that are basically impossible elsewhere.

Finally, while the infrastructure could be better in many places, things are constantly improving; newer developments (housing, malls, Olympic sports venues, etc.) have bicycle parking as a standard feature, for instance.