Rock climbers typically carry several circular slings, necessary for fashioning protection as a pitch is surmounted. These are routinely carried over one shoulder and under the opposite arm. This avoids the possible noose effect in a fall or entanglement. I certainly wouldn't just drape something around my neck unless it had a breakaway joint. You put it well - why put your neck in a noose?

I also remove my wedding ring and wrist watch when climbing. I have only seen deglovement injuries in pictures and I don't wish any personal experience. I usually carry the ring on a light sling worn like my climbing slings.

In really thick brush, I could readily see a cord worn around the neck being caught, with somewhat nasty results.