The idea of through-running is to not have trains parked like that in an over crouded midtown. That way they can reduce the number of tracks and widen the platforms. It has beem done with great success in many big cities already. The idea would be to have NJ Transit trains run to platforms at their rail yard in Queens. This is a large ripe for development area between Long Island City and Sunnyside Queens. It could also go farther to Port Morris in the Bronx and link with Metro North and the further North East rail corridor. Long Island Rail could go to a new terminus rail yard in NJ which could have a bus terminal to reduce the amount of busses into NYC. The main issue I can see is some of those commuter runs are too long for crew rotations and may require crew shifts who just do last stop in NJ through to the outer boro NYC rail yards.
Here is the group advocating this idea. Rethink Penn Station NYC https://www.rethinkpennstationnyc.org/