If you look at Gilbert and Sullivan, they were played to be the English equivalents of Jacques Offenbach's operettas. They're full of gags, funny situations and parody, which was the typical humor of the time.

The 'H.M.S. Pinafore' is popular because it's funny. It feels good in its own time. That way it can provoke laughter, when we can translate it to another time and place.