They should not be allowed in the sidewalk because they’re a hazard to pedestrians.
Bicycles are to pedestrians like cars are to bicycles. Every argument you can make about cars endangering cyclists also applies to cyclists endangering pedestrians.
Bicycles belong in the road because their speed is more similar to cars than pedestrians, their (lack of) maneuverability is more similar to cars than pedestrians.
Clearly three separate protected rights of way would be better than the current two
Cyclists on the road are supposed to use hand signals to indicate turns, just like cars whose blinkers are not functioning