Actually it probably would be hard to route traffic through Poughkeepsie, at least traffic headed for NY City. Traffic headed north might do ok by crossing that bridge, but traffic headed south would have a tough time reaching the city. To my knowledge, the remaining tracks heading southbound are all owned by Metro North at this time. Metro North's commuter service is quite heavy and there is little room for many extra freight trains.
Even if they do get down to the Bronx, there is only one remaining track into Queens, which in turn would then service Queens, Brooklyn, Manhattan (via truck), and Long Island.
So a 70+ mile detour to the north, followed by the same heading south in congestion would not make more sense overall in the scheme of things, than digging a new tunnel direct from NJ to Brooklyn.