The above was from last Sunday around 17z. I was watching FR24 with the ATC feed. The airport was operating in 'arrival priority' with approaches to both 13L (Canarsie) and 22L.
Both directions were offered their respective VOR approach. Authorized carriers such as JetBlue and Alaska Airlines requested the RNAV RNP 13L (not publicly published by the FAA, yet).
My question is why wasn't the ILS offered for 22L? I checked the NOTAMs and the serviceability of the ILS was not there. And since the VOR is an instrument approach, it wouldn't quite fit the visual vs. instrument asked about here. A 4-year old post on airliners.net blames LaGuardia (LGA):
JFK will frequently land with max crosswind or tailwind components and frequently uses off set VOR approaches to minimums before switching to the preferred ILS.
Why? LaGuardia and the airspace to the north.
While yes the VOR is offset (232° vs. 224°), it's not a big offset that would free a chunk of airspace for LGA when it vectors its inbounds via a left downwind for runway 22. To be sure I superimposed both plates by aligning the 604' structure (shown below).