They were never 'unaccompanied'. The earliest rhythms were work rhythms (3/4 being the rhythm of scything...see RVW for more info)and the work rhythm was vital to the singing, whether on the farm or on the ship, and singers would move in accordance with the rhythms to which the songs were attached. If you mean 'without instrumental backing' , then that's because its difficult to play and work at the same time. When the song's moved indoors, the musicians, who normally already played for dancing, would sometimes accompany, but it wasn't necessary. Revival singers, such as martin carthy, took old songs and put wonderful guitar accompaniments on them...because he could!
   The Copper repertoire includes songs that may have had an organ accompaniment if the songs were learned in church, but at home,or the pub, unaccompanied was the only option, not a shibbloeth.