"as far as I am concerned, such silly, childish ditties have absolutely nothing to do with folk music."
Some songs with actions, like 'John Brown's baby's got a cold upon his chest', have been around a long time (since the 1920s?) and used in all kinds of contexts - schools, community singing, parties etc. etc. - often spread by word of mouth. I'd reckon such a song has a good claim to be a folk song.
There's plenty of folk songs that are fairly nonsensical and maybe they haven't been given their due as a genre. Isn't nonsense always a bit subversive?