Just to toss a couple more opinions into the stew...

When a club or venue specifies "absolutely no instruments" for a particular evening, that may not be snobbery. It might be that if they leave it open, they feel the instrumentalists might "take over" or something. In a disorganized sing-around, an instrument also helps a person jump in for their turn (perhaps overriding someone who is vocal only) by launching into a couple of introductory chords. Also, heavily instrumental arrangements may "desensitize" some audience members to vocal subtleties - at first blush, a vocal-only presentation following a band may seem bland, especially to the Great Unwashed Masses. There are probably many more options for instrumental or combined instrument/vocal performances, and relatively few for primarily-vocal without accompaniment - so perhaps they want to stand their ground and say "for THIS evening, NO instruments." Seems fair to me.

As for singing while accompanying yourself, I think it takes both talent and practice to have GOOD instrumental and GOOD vocal at the same time. I suspect just about everyone would say they can put more nuance & subtlety into their performance if they only focus on one or the other.

There is one other variation that doesn't seem to be talked about much so far in this thread ... a duet or ensemble where vocal & instrumental duties are divided. Thus you have the benefits of accompanied singing (pitch reference & more complex arrangement) while still allowing each performer to focus entirely upon their particular part. Of course, that usually DOES call for a bit of prior planning and maybe even making friends with other performers rather than isolating yourself in your own music [grin].

-Val
who sings middling well while playing guitar, rather poorly while playing harp, & generally plays or sings better when that's all I'm doing.

(For those keeping demographic score, I'm in the US)