Two reasons: First, cost. A mile of subway construction costs ten times the cost of a mile of elevated construction. Today as well as in 1910. PRR built the East River tunnels primarily to access a coach yard that could be constructed where land was (then, not now) cheap, off Manhattan and in Long Island, and second, to provide Manhattan access for Long Island commuters and thus placate the Albany Legislature to control the then NIMBY's since this politically unified the great Empire State tieing passenger rail on Long Island to the mainland. The through service to New England was a third reason but not anywhere as important as the first two. So once the PRR East River tunnels were constructed, it was a lot cheaper to contruct a Hell Gate Bridge and the embankment and elevated structure to tie into the existing Harlem River branch of the New Haven than to build a new north-south subway in Manhattan.
Second, the line was built for freight service as well as passenger service. The Long Island already had a car-float operation going at Bay Ridge, and the New Haven could drastically reduce its operating costs by using the LIRR facility to replace the car float from the south end of the Harlem River Branch in the South Bronx. This cut the water distance by 80%! So the New YOrk Connecting Railroad built the Hell Gate Bridge, the embankments and el structure, and connecting tracks, and was owned jointly by the PRR and NYNH&H. CSX, CP, and posibly the Providence and Worcester, still use the bridge for freight, interchanging with the New York and Atlantic, freight operator for the LIRR, at Fresh Pond Junction and yard in Queens. The other connection for the New York and Atlantic is New York Harbor, which now runs the car float from Bay Ridge, Brooklyn, to Greenville, NJ. where it connects with Conrail shared Assets.
There is no pedestrian access accept for railroad personnel on the Hell Gate Bridge at the present time. I think the Triboro still has pedetrian walkways. This included access to the island, but I am not sure that this still exists. The 60 bus ride should tell you a lot and is recommended, and is an excellent way to access Manhattan from LaGuardia Airport. On 125th Street it connects with issues transfers to the Broadway 1 line at Broadway, the A, B, C, D, 8thAv/6thAv lines at St. Nicholous Avenue, the Broadway-7th Avenue 2 and 3 at what was called Lenox Avenue and is now I think Martin Luther King Boulevard, and the Lexington Avnue 4, 5, 6 at Lexington Avenue. In addtion, there is nearly ALL (exception a few rush hours super expresses) Metro North service at 125th Street and Park Avenue, with a ten minute ride to Grand Central Terminal.