Hell Gate Bridge was a critical part of PRR's New York Tunnel Extension Project, which included the New York Connecting Railroad. The NY Connecting RR was designed to allow access through Penn Station for passenger trains from the south and west directly to the principal cities of New England and Canada via what is today known as the Northeast Corridor. Fright traffic came mostly by carfloat to Bay Ridge, and from there over Hell Gate bridge.
What Amtrak route are you referring to? Remember that before Penn Station and the Tunnel Extension Project in the first decade of the 20th century, there was no direct connection to Manhattan either over or under the Hudson. Gustav Lindenthal, who designed Hell Gate Bridge, had earlier proposed a huge bridge over the Hudson in 1899, but the Hudson River tunnels prevailed in the final design.