Just thought of one other fair reason for a solo performer to accompany him/her self on an instrument, which I don't recall seeing yet in the discussion (apologies if I overlooked one of the posts) -

It fills in a space between (or within) verses to allow for catching a breath, or to give time to rack your brain to remember the words of the next verse!

Val
(whose motto is "That wasn't a mistake, that was Jazz")