I used to think as you do concerning the pavement. However, experience cycling[1] has taught me that the pavement is not a safer place to cycle. Cars expect slow-moving pedestrians on the pavement, not fast-moving bicycles. Consequently, cycling on the pavement leads to a lot of collisions with cars as they pull in/out of driveways.
[1] In Oxfordshire, UK -- this may be inapplicable to the US.
You go as far as to say that riding a bike on a sidewalk is not a safer place for the bicyclist as compared to riding it on a roadway along with cars? I'd expect you to be in a minority in this, your experience must be very different from mine.
The way I see it - if my 13 y/o daughter takes a bike to go to convenience store a couple of blocks down the street to get some ice cream with friends - I sure hope she breaks the traffic laws and stays on the sidewalk.
I don't know if it's safer but it is still really stupid to use the sidewalk. Not for a kid, your 13-year-old would not be told to use the street.
But I live in Chicago and, like you, used to think that it would be safer to be on the sidewalk because of the really stupid drivers that we tend to have here. A few days after making that decision, I nearly hit a person coming out of their house. There was no way for me to see them and not way for them to see me. As a pedestrian, I've been nearly hit coming around corners and I also barely managed to avoid getting hit from the front by a jackass who wasn't paying attention.
It's just not very safe for the pedestrians. There are so many circumstances where it's impossible to avoid a collision.
Although I will say that I am shitting bricks every time I ride on the street, even if I am on a bike lane. Most drivers are really good and they pay attention, but there are some that are just fucking stupid. They have no idea what the laws are and they think a bike should be on the sidewalk so they drive erratically to get me off the road or they honk and yell at me even though I'm doing everything right.
Yes, I would go that far. But, as I said, perhaps my area is unrepresentative. There are quite a lot of cyclists in Oxfordshire. If you cycle on the pavement, the cars don't expect you. If you cycle on the road, they usually do.
I suppose I should add the caveat that very young cyclists are better off on the pavement even here. When I take my little sister to the shops, I have her cycle on the pavement. That's because she can't cycle in a straight enough line for the roads to be safe.
Most places in US children (and adults on bikes accompanying those children) are allowed to ride on sidewalks by law. I do find it safer to ride on the roads though mainly because of dogs, joints, and car's from driveways and making right turns. But the main concern is that on a sidewalk if I were going as fast as on the road I would be a danger to not only myself but other pedestrians.
[1] In Oxfordshire, UK -- this may be inapplicable to the US.