I second the sentiment that it's not necessary to sing the whole song unless omitting a verse would leave the story incomplete or miss the main point of the song.

In earlier centuries there may have been a demand for longer songs. People didn't suffer from "entertainment overload." But it's hard to keep people's attention much beyond 3 or 4 minutes with a song now.   

Also, some songs have a virtually endless supply of sequence-unimportant verses.

Geoff, as for adding verses, I think it's different when the "original" is trad. or author unknown.   The folk process involves improvising, either by accident or by design.
Oh, and people have been known to add a verse for other reasons than "because I am a self-important prig."   They may want to "update" the song* or make a one-verse + chorus song a bit longer - and if others pick up and sing that new verse, it's obviously not because of vanity.    My appraisal would depend on whether the new verse "fits" or not. The new verses don't always spoil the original.

*E.g., Joni Mitchell's song "The Circle Game" ends with the boy being 20 - about Joni's age when she wrote it. I've often wished she, or someone else, would add a verse from the perspective of someone closer to "the last revolving year."
On the flip side, I heard someone do a time-constrained version of Harry Chapin's "Cat's In The Cradle" recently, and she omitted the college-age son verse, and the story came through loud and clear without it.