The reason I think this is important in this question is because:
1) I strongly suspect washing your hands isn't merely about washing off whatever got onto your hands during your bathroom trip, but also whatever got on your hands since the last time you visited the bathroom.
2) There are plenty of studies, going back to Ignaz Semmelweis in 1847, showing hand-washing has practical results, but there may not be many studies showing how to use the bathroom without handwashing.