The LAX-JFK and also SFO-JFK are three class flights designed to compete for a certain demographic that frequently flies from those city pairs and pays for a premium first class service. Can you guess who some of these people are?
My UA source says they have no problem selling FC on these routes and that they are also very profitable routes. I think most of the majors run three class on these routes; I know AA does with it's Flagship service.
If you did not mind the extra connection, IMHO even C class is nicer than F on the two class flights.