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As some comments say on that page, there are numerous technical details as to why it isn't nearly as simple as proposed. AFAIK you can't easily run LIRR trains to NJ because only a few engines support catenary operation, everything else requires a third rail to be built.

So while this might get us a few percent increase in the number of trains for now, at the cost of a few hundred million to build out third rails in NJ (or catenaries in LIRR areas where NJ transit trains might be routed), it doesn't change the fundamental infrastructure issue given the growth of mass transit in the NYC metro area.