Err.. the Navy are in charge of the program because it's a Marines operated aircraft (the Marines are part of the Navy not the Army). The US Air Force in fact operates very few helicopters and like all air forces has very little interest in anything that isn't pointy and goes really fast.
They actually did do a competition for the VH-71 program, it was between the Sikorsky S-92 and the EH-101. The 101 won, however at that stage they really didn't have the full specs of the program just a few basic ideas like performance envelope and size of the cabin (the latter being where the 101 really excelled), this was due to the desire to replace the ageing Sea King airframes as rapidly as possible.