The current public transport system in JFK is that you need to take a train to Jamaica station and then switch there for a train to downtown New York City. This makes it quite inconvenient (especially if you need to switch to another line later on) and makes taking a taxi more attractive time-wise unless it's rush hour. In comparison taking the train downtown in a city like Vancouver can be faster than a taxi at almost any time of day.
What's the historical reason behind not allowing direct trains to JFK? Or perhaps one is planned for the future?