The random danger of NYC is part of its allure. People also benefit from appropriately challenging physical environments, as it enlivens and engages the body. Inattention in dense environments can lead to conflict and congestion, and so I suspect that the random observable dangers can serve some public good by causing general awareness and the self-exclusion of those who do not adapt to the needs of a dense place.
Another advantageous random danger in NYC is the roving squads of ninjas. Good opportunity to keep practicing your nunchuck skills.
Friend of mine when he lived in Greenwich, CT commented on the "roving bands of preppie youth."
I think they were mostly harmless :-)
They might grow up to be managing directors at Bain Capital!