Living in the city is one of those places where the statistics sound nice but not going off your intuition eventually catches up to you.
(The stuff about firefights similarly confuses this -- I have no doubt that the NYPD is afraid of getting into gunfights. But that has absolutely nothing to do with the routine paperwork of recording a homicide victim.)
Intuition is meant to comport with ground reality, and the ground reality is that NYC is not gangland anymore (and hasn't been for decades). Other cities might still be, but we aren't.
Ultimately recorded crime data should be used as an aid to guide our decisions, in combination with other signals. I would consider your view reckless in light of deciding how to go about my life in the city, but ultimately it is your decision to make and I hope it guides you well.
* “Like NYC” is doing a lot of work here. NYC has organized crime, but not a lot of violent organized crime anymore. There’s a reason the handwringing over MS-13 focused on the suburbs of Long Island and not NYC.
* There’s a lot of “it just doesn’t feel right to me” floating around whenever someone points out, statistically, that NYC is both far safer than its recent history and far safer than the rest of the country. And it’s perfectly reasonable that people would feel that way, because it is unintuitive! But unintuitive feelings don’t trump numbers, and there’s no real evidence (including from sources that have a strong incentive to make crime seem as bad as possible) that massive amounts of violent and property crime are going unreported.