Greene seemed to have little interest in politics or the military post war. He was also heavily in debt and poorly ran his plantation. Civilian life didn't really seem to suit him.
Although I'd say he's do we'll as secretary of war and build his political position from their, I question whether Washington would give him the position considering he gave to his close friend Knox.
There's also the issue of Greene being against slavery early in his life. He changed it later, but many would remember he was against it at one point.
