In America, this type of seating became largely obsolete in the mid-1930s when cars became too fast and streamlined for the comfort of passengers in such a seat. Their popularity was further diminished by frequent injuries, including decapitation that sometimes occurred in accidents. Rumble seat passengers were essentially seated out in the elements, and received little or no protection from the regular passenger compartment top. It is possible that the last American-built cars with a rumble seat were the 1939 Ford and 1939 Dodge and Plymouth. Prior to World War I, a single, center-mounted rumble seat was sometimes referred to as a mother-in-law seat.
I wonder if putting children in a rumble seat today would be considered "child abuse?" The times were certainly much more simple in the 1940s.