"so you can fill more land in by Flushing Bay"
The NIMBY's got a Federal Court to block attempts to build the "West Way" because of some fish that lives underneath the old Central Rail Road Piers on the West Side, filling in Flushing bay is not realistic in a City like NY.
If Heathrow can handle nearly twice as many passengers a year as JFK
with one less runway then there is plenty of room for expansion, even Newark airport has land where two more runways could be built.
Before they would ever build a new airport they would build another runway or two at both EWR
for a fraction of the cost of building an entirely new airport, LGA
is in too tight a corner between Rikers Island and nearby neighborhoods to ever be expanded.
Besides the NIMBYs surrounding the airport you have the Mets who already have to tolerate the noise and the US Open, and forget about trying to aquire Rikers Island for expansion.
You think trying to build a new runway is hard, try re-locating the largest "jail" in the World. The only places where Rikers could be relocated would be Governor's Island (does not fit redevelopment plans) or Staten Island, and Staten Island would riot and finally succeed from the City if they tried to move the City's jail to the bourough who for decades had to put up with the "city's" garbage.
another runway could be built where the East cargo buildings are located to the East of 13L, the mostly older cargo buildings could easily be relocated to the West Side of the Airport.
another 9,000 ft runway could be built on vacant land between the NEC and Rts 1 and 9, the only real obstacle is the Anheisure Bush brewery which would have to be moved. Also 22 L could easily be moved across the Turnpike on land now occupied by Conrail Shared Assets and used as a yard, the Port Newark Rail yard could easily be relocated and the "new" 22L could be far enough from 22R to allow for simultanous landings and take offs.