A few years ago I was in Luzern (=Lucerne), Switzerland; I noticed the aftermath of a minor traffic accident between two cars. After the two cars departed, there was some broken glass left in the street, the policeman on the scene, took out a broom and pan (from his trunk) and swept up the glass. I just can't see a NYC policeman sweeping up broken glass--it would remain in the roadway until the next time road sweepers came through.
Not just NYC. I can see you applying this to any city in the US and the results would be the same. It's a matter of "culture," and it's different from location to location, especially if you bring in the Internationals.
In NYC, we rarely make eye-contact when we walk down the streets, but I was a small suburb in New England last week and everyone said "good morning" to me as they passed me. It was a shock at first, but at the end of the week, I was saying "good morning" back. I got so used to it, I said "good morning" to a random stranger today on 34th Street and they gave me a look as if they were asking me "do I know you?!"