Actually, that verse didn't go into the trash can immediately, as shown by the fact that the 1771 text referenced above not only retains it but adds a quatrain to it, and later reprintings of the text, whether as a "song" or not, were still prone to include all seven original stanzas. There is no real evidence to support either your or my suppositions of impropriety. More likely, the driving force to omit that quatrain was simply to pair them, as required by settings like Lockhart's, or to shorten the text (as shorter songs became more the fashion.)

The evidence is overwhelming that people revel in songs reflecting a "deeper nastiness of character." Sanitizing such sentiments is left to fearful collectors, hypocritical religious zealots, and overactive government censors. In fact, any polite song seems to spawn coarse parodies almost immediately, due to our need to drag such artificial creations down to our own level. So climb down from your ivory tower, turn on the radio, drop into a pub, visit a school yard, gather around a campfire and listen to the songs that people actually sing before you assert that we dislike a surface expression that betrays a deeper nastiness of character. It's the basis of most of our songs!