NYC has a FUCKTON OF PEOPLE. And crime isn't uniformaly spread among it all. Some small sub-sections could be accounting for dispraportionately more than others. So with both of those things, the liklihood of a crime happening is very high. But not per 100k people.
That's the big difference. If there is 1 shooting per 100k people, and there are 5 million people around, that's 50 shootings. Vs if you have only 10,000 people around. At 10,000 people, you might see a shooting every 5 years, but proportionately that's double the NYC rate.
That's where the visibility vs reality is so counter-intuitive.
Also interestingly enough, I see A LOT of homeless (I work near a shelter). And they are indeed crazy looking. But honestly the worst they do is yell at you, and often its because they haven't had real human contact in months. Just imagine being isolated inside a massive crowd.