actually, the blues started off as a field holler by transplanted slaves, and this was unaccompanied. Leadbelly was the first folk artist to accompany chain gang songs,
related to the field holler. Vera Hall, one of the great African-American folk singers sang unaccompanied. Her "Boll Weevil" is a classic.

The African-American spiritual was sung unaccompanied and later reoriented instrumentally into the church gospel music.

I agree, however, that bad musicianship can louse either acc. or unacc. singing.

A notable example of unaccompanied singing was the opening of Oklahoma, where Curly sings unaccompanied, "Oh What A Beautiful Morning".

Iron Head Baker was one of the great chain gang singers who had no accompaniment.

What we know of the blues today is basically the Chicago electric guitar school popularized by Muddy Waters and Big Bill Broonzy, who later went acoustic. The origins of the blues are decidedly unaccompanied.