NYC gets dozens of millions of visitors annually, in addition to people commuting in daily and people transiting through the city. So, while the number of crimes is high, the number of people actually in the city at any given time is multiple times the number of people who reside there. Probably the total number of people in the city anually is 10x the people who live there.

I'd also factor in the numbers are higher also because policing is very robust. I can't think of any other city where I saw a cop nearly as often as NYC, they're everywhere.

Anecdotally, I never felt unsafe there. Although where I grew up crime was rampant, common, and expected- so comparatively NYC seemed really safe, and it wasn't hard to avoid high risk places/situations. I do think people hype up the crime numbers, and forget to consider the variables present in a megalopolis which aren't present in smaller cities.