Well, I can't sing and play the trumpet at the same time.

But I suspect that it started because people wanted to sing (for any reason) and just decided to do so. My family has always sang or whistled as they worked, and I'm sure that others did the same. We did it in the Army and it helped shorten the miles we walked. Shanties were sung for a variety of reasons, and lightening the task was one of them. Ditto for working the farm fields.

Music, like laughter, kills lonesome.