The comment above about the 'hillbilly' aspect of this song is the clue. The whole point is to make fun of the unenlightened rural conservative folks that "aren't like us" (anymore), and was a staple of a time when the "post-war" was changing into the "boom times" of the 50s. It's instructive to remember that the old ways, which included strict child-rearing (and wife-beating), were giving way to many of the attitudes we see above -- "How could anyone think this funny?" and so forth.

You could probably make a list of other kinds of song that came out of such "change-times", not limited to "coon songs," "stage Irish songs," etc. If I were in graduate school again, it might be fitting for a thesis.

So remember the times and the reasons for this and similar songs.

Bob