In my opinion if a sidewalk is available then bicycles absolutely do not belong in the street with motorized vehicles. Where sidewalks are not available, then bicycles can use the road or be walked on the shoulder.
I looked up the bicycle laws for my state and the only thing I could find possibly relating to bicycle operation on sidewalks is this.
IC 9-21-8-37 Pedestrians and children; due care; caution
Sec. 37. Notwithstanding other provisions of this article or local ordinance, a person who drives a vehicle shall do the
following:
(1) Exercise due care to avoid colliding with a pedestrian or a person propelling a human powered vehicle, giving an
audible signal when necessary
(2) Exercise proper caution upon observing a child or an obviously confused, incapacitated, or intoxicated person.
http://www.bicycleindiana.org/images/Indiana_Bicycle_Laws.pdf
That seems reasonable enough to me. Unfortunately there are a lot of areas I drive through that do not have sidewalks.
What gets me is that Indianapolis has started putting bicycle lanes in the streets downtown where there are very wide sidewalks. This has caused the loss of a motorized vehicle lane and confusing lane shifts through multiple intersections on some of the most heavily traveled inner city roads. The bicycle lane actually crosses turn only lanes and temporarily travels in the middle of motorized traffic. This is a considerable hazard to both bicycle riders and motorists.
Since the bicycle lanes were installed I have had at least 20 near accidents with other motorists who were not paying attention to the lane shifts, the first 4 of which were the fault of public transportation operators. I have only my defensive driving skills to thank for not having a collision yet.
I have seen cars parked in the bicycle lane and police using the bicycle lane to pass other traffic.
It has gotten to the point where everyone apparently ignores the lane shifts and drives where the lanes used to be simply because that is the only safe way to navigate the street.