Mike2,
I think you summarized the issues pretty well.

This discussion has gotten long, and I think we may have forgotten
SongBob's original post and query.

It was pretty clear to me that he was talking people singing in informal or at least unpaid settings, not professional gigs.

I agree with Bill D that if I can close my eyes and not tell whether a book or lyric sheet is being used, its presence is no more disruptive than teleprompters are when used by skillful professionals delivering the news or a speech.

And, Don M, I like the way you think! LOL

You're right, of course, that a true professional doesn't let the audience know it when they flub their lines or lyrics.
But, as I said earlier, every time you improvise, increase the likelihood of flubbing the line again. If the original script (lyric) was really good, this "folk process" will probably make the song (or play) worse, not better. That is one reason for using some sort of cue card. But if you use it right, it will hardly be noticeable or lessen the impact of your song.