Landing a aircraft at the wrong airport is a huge cost for the airline. They don’t do it because gates are occupied. Jfk is just as gate restricted as LGA. You also now have a crew at the wrong airport and a outbound flight you have to cancel. It’s a very expensive decision.
Why would they go to JFK? Thrust reverser issues, brake issues, flap issues, slat issues, NWS issues, trim issues Navigation equipment issues ect... There are many possible reasons.