Metrics-driven policing often gets the blame here: shifts in policing policy that hold individual precincts, officers, etc., directly responsible for crime statistics under their watch were initially successful in more efficiently allocating police resources, but have now created a set of perverse incentives that encourage officers to either not file reports or to down-classify reports into less-grave categories (reporting armed robbery as theft, etc.). These kinds of programs originated in NYC, as the "CompStat" program under Jack Maple and Bill Bratton, largely during the administration of Rudy Giuliani as mayor, but similar programs have since been adopted by (particularly urban) police departments across the country, to arguably similar both positive and negative effects. This kind of stats manipulation ("juking the stats") featured heavily in the TV show The Wire, for example, which is set in Baltimore.

So, to more directly answer your second question: other cities absolutely also suffer here, but New York has been at it the longest, and so is perhaps best known for this issue.

For more background, Reply All did a two-parter a few years ago exploring the history here, which is quite good. This is the first part: https://gimletmedia.com/shows/reply-all/o2hx34