I enjoy singing both with and without accompaniment. I do find that as I (usually with Linda these days) do quite a lot of singing in pubs, to non-folk audiences, that a guitar can act as a "bridge". We will nearly always start off with the guitar, but once we've got the audience's attention/confidence, we will sing a fair amount of unaccompanied material. We often find that some audiences seem to think that unaccompanied harmony singing is quite a clever accomplishment. I also find that it's much easier to act and move around without a guitar, when I'm singing some of my comic music hall material.

There is a fair amount of tradition gospel material available over here in the UK - much of it rather akin to the american "Sacred Harp" tradition and these days we tend to call it "West Gallery Music". It was not always unaccompanied because there was usually a band (often consisting of a very strange assortment of instruments) as well as the choir. The band and choir would usually be accommodated on the gallery behind the congregation - a much better place from which to encourage them to sing, than the modern day choir stalls out at the front. When the choir were about to sing an anthem on their own, the congregation would be invited to "Stand and face the music" - a phrase we still use today. There are "West Gallery" choirs, bands and consorts all over the country these days and "The Mellstock Band" give an idea of some of the sorts of music (and background stories).
Incidently the melody of "On Ilkley Moor baht 'at" comes from a West Gallery tune (Cranbrook by Thomas Clark of Canterbury) and was originally used for "While Shepherds Watched".