I have various shawl-type things around here, inherited from my Irish aunt and relatives in Connecticut, and they seem to naturally want to be doubled over and worn over the shoulders that way. The round shawl wouldn't need to be folded perfectly in half, but at 3/4 it would give a nice "collar" effect and drape from the shoulders.

I have an alpaca poncho that has the hole in the middle of the big square of fabric, meant to be worn over the head. But that neckline is specifically finished to be worn that way.

SRS