"a capella" implies a certain kind of formality which unaccompanied does not. To call some kinds of singing and some kinds of songs "a capella" just because they don't have instrumental accompaniment borders on the ridiculous.

"After the game we all had an acapella rendering of Eskimo Nell and similar ditties." "The sailors struck up an a capella sea shanty." "Leadbelly sang John Henry a capella on this occasion."

I remember years ago the first time I ever heard real Gospel Singing, with an American choir on tour. They may have had some kind of piano going some of the time - but if so, you wouldn't have even noticed it.

The basic thing with accompaniments is, they shouldn't stand in the way of the singing. With some types of singing that'd be because it's wrong to risk interfering with the singer. With gospel it'd be because the instrumentalist who got in the way might get run over.