According to the FEIS, Hanover Sq was chosen as the southern terminus of SAS since a station at South Ferry would not have made a future extension to Brooklyn possible, would've had lower ridership and would've resulted in construction impacts to Battery Park.

From Appendix B: Development of Alternatives, p. B-30

The first two alternatives considered would provide service as far south as Whitehall Street and allow for transfer passageways to the N R service and to the 1 9 routes. These options would have two stations south of the Brooklyn Bridge: one at either Wall Street or Maiden Lane, and the other at Whitehall Street. In both options, the tunnel and station would be very deep (85 feet or more below the surface) to allow the route to pass safely beneath existing tunnels, resulting in long travel times for passengers exiting the station. Only one of these, the option with the Maiden Lane station, would permit future connections to Brooklyn. These alternatives were eliminated in part because they did not attract enough riders, given the Whitehall Street Station’s distance to large office buildings and depth, to offset their higher cost in relation to the other options. In addition, these options would have resulted in impacts to Battery Park and Peter Minuit Plaza. They would most likely involve construction activities required for the terminal below and for possible vent structures, emergency exits, and/or station entrances into or near one or both of the parks.

And from Chapter 23: Response to Comments on the SDEIS, p. 23-24

Comment 52: The project’s southern terminus should be farther south than Hanover Square. The termination north of Whitehall Street does not allow for service diversions. Why was the Whitehall terminus/station eliminated? (Shachter) The Second Avenue Line should run through the South Ferry line and have a South Ferry terminal. A provision for Brooklyn service could be made at South Ferry. (Hassan, Kupferberg) Response: The Hanover Square Station is being designed at a depth that would facilitate a future extension to Brooklyn to be constructed deep in rock. In the interim, storage tracks are proposed south of the Hanover Square Station, which would allow trains going out of service to layup during the midday and overnight. The train storage would not be feasible if the Second Avenue Line were extended to a terminus at Whitehall Street. Continuing the service westward past Whitehall Street would be very difficult, because of the presence of numerous other tunnels in this area (which include three subway tunnels that pass under Water Street on their way to Brooklyn, the Brooklyn Battery Tunnel, and the Battery Park underpass). As described in Appendix B, two alternatives were studied that would provide service as far south as Whitehall Street and allow for transfer passageways to the N R service and to the 1 9 routes at South Ferry. These alternatives were eliminated because they did not attract enough riders, given the Whitehall Street Station’s distance to large office buildings, to offset their higher cost in relation to the other options. In addition, they would have resulted in impacts to Battery Park and Peter Minuit Plaza. These alternatives would have required possible vent structures, emergency exits, and/or station entrances into or near one or both of the parks. Minimizing impacts to both open spaces was among the reasons considered in selecting the terminal location.

The 1970s plan for SAS did however include a station at Whitehall St. But I'm unsure whether that version of the line was designed to be extended into Brooklyn.