Why is there such a long displaced threshold on 22R at JFK/KJFK?
Its to maintain proper clearance over the park on approach from the north and avoid trees. They tried to extend the runway in 2013 but were ultimately denied due to minimum altitudes. Its covered in the October 2013 document Runway 4L/22R Improvements John F. Kennedy International Airport    

They submitted for 


  
  Relocate the displaced landing (arrival) threshold on Runway 22R 3,316
  feet to the north.
  


but ultimately... 


  Two of the elements, the relocation of the Runway 22R arrival
  threshold 3,316 feet to the north and the relocation of the Runway 4L
  end (departure starting point) 460 feet to the north, would have
  resulted in aircraft being at lower altitudes than existing conditions
  over areas to the north of the runway, including Idlewild Park. The
  lower altitude of aircraft would have resulted in up to 800 trees in
  Idlewild Park becoming obstructions, as defined in FAA Order 8260.3B,
  United States Standard for Terminal Instrument Procedures (TERPS). FAA
  Order 8260.3B specifies the minimum measure of obstacle clearance that
  is considered by the FAA (the Federal authority) to supply a
  satisfactory level of vertical protection for aircraft operating at an
  airport. If the project described in the May 2012 Draft EA were to be
  implemented, up to 800 trees in Idlewild Park would have required
  removal to comply with FAA standards. The project described in the May
  2012 Draft EA has been modified to avoid this impact as explained in
  the following paragraphs.
  
  In order to minimize the number of trees to be removed from Idlewild
  Park, the Port Authority made the decision to redefine the proposed
  project as described in Section 1.3 of this Revised Draft EA. The Port
  Authority no longer proposes the relocation of the Runway 22R arrival
  threshold 3,316 feet to the north. The arrival threshold on Runway 22R
  would remain in its existing location, which does not result in lower
  landing elevations north of the Airport.