Why does an Airline have to get permission to accept a LAHSO clearance? What is so special about the actual manoeuvre?
Authority (or lack thereof) for LAHSO is in the Ops Specs specific to the particular airline. A LAHSO clearance issued by ATC even when allowed by the book is still ultimately accepted at the Captain's discretion.
JFK can be a bit of a jungle but at times you have to wonder if everyone actually has the taxi chart out and is not just relying on ambiguous yellow signs and the tender, thoughtful instructions given by ground control to stay on the straight and narrow.