The problem is that bikes are not welcomed on roads by most drivers, at least in the United States. If drivers viewed bicycles as vehicles, there would not be a need to construct bike lanes and bike paths. It has been shown to be safer to ride in the motor vehicle lane rather than in the bike lane or shoulder for two main reasons: (a) debris is more common on the side of the road and (b) drivers are more likely to see you if you are in front of them. Before you ask what happens on a two-lane road with no opportunities for passing, it is my understanding that bikes are required to move to the side to let cars pass when practicable (safe). Many states also have a law that a slow vehicle must pull over if possible to let vehicles behind pass if a certain number (five?) are backed up behind it. This is mainly aimed at farm equipment but would also apply to bikes.
Of course the sidewalk is right out because of pedestrians (it is usually illegal to ride on the sidewalk for this reason).
If instead of striping bike lanes, the department of transportation would construct a wider right lane than normal, about the same width as a regular lane plus a bike lane, this would allow bikes to ride in the normal lane and move over to let slow traffic pass if neccesary. On a multilane road, bikes would usually not even have to move over.
Source: some recent discussions on the usenet bicycle newsgroups (crossposted to misc.transport.road)