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.
Yup.
I will say this, however, it's rare to see broken glass in the middle of the street. Maybe you'd see it near the curb if some car were unlucky enough to be burglarized.