> I don't feel safe biking on the street, and would rather stay on the sidewalk like I did when I was a kid. I would just have to pause to check before crossing driveways and intersections.
This is a common misconception among folks who don't cycle. Cyclists are actually safer on the street. If you ride on the sidewalk, you have to deal with more potential issues such as pedestrians, driveways and intersections become even more dangerous because you're behaving as both a pedestrian and a vehicle with the all the disadvantages of both. In general, cyclists are the most unsafe where cars are not expecting them. Large suburban parking lots, for example, are particularly hazardous for cyclists-- experienced cyclists use extreme caution in parking lots, believe it or not.Cycling is not particularly dangerous, depending on how you define "dangerous".
Most car-bike collisions occur at intersections and are "right-hooks". This is when a car turns right, cutting across the path of the the cyclist and the cyclist hits the car because there's not enough room to stop or turn. These accidents typically result in bruises, damage to bike and sometimes a broken collarbone. They're rarely fatal unless the right-turning vehicle is a truck and the cyclist ends up under the truck.
The accident you're probably thinking of is a car hitting a cyclist from behind with a huge difference in speed. This, I believe, results in the most fatalities for car-bike accidents. It is relatively rare.
> ...what chance do you have from a physics standpoint to be truly safe...
None. You have no chance to be truly safe. That's an unrealistic goal for any kind of traffic system.