You have to deal with the AirTrain (which isn't free) at JFK. The Tube actually has a Heathrow station, and the RER goes directly to CDG. It's even easier to get to Gatwick than JFK.
what's the problem with the airtran? it's rare to get to lower Manhattan faster with a taxi than via subway even with congestion pricing. and the cost will be at least 10x.