The Dulles train I think you refer to is within the airport - it is not leaving the security perimeter.

New York is not a good comparison as JFK is international hub but La Guardia domestic. I don't think you would find much support in the Big Apple for splitting JFK traffic between 2 hub airports (Newark?).

BTW, JFK flights take off over the sea (and they manage bird strike issues.) It also has lots of space, more terminals and runways than Heathrow.

Schipol is surely a better European comparison and has many more destinations than Heathrow already. You hardly notice the air traffic even quite close to the airport.