Regardless of the probability of someone grabbing it (although apparently this has happened to you several times)
Not sure where you got that from. It has never happened to me. I haven't seen a plethora of reports of people grabbing someone's bungeed alternate, either. Those contribute to my feeling of relative unconcern about the prospect.
Also contributing is that I bungee mine as close to my neck as I can without it getting in the way or being uncomfortable. Partly to make it possible to catch it in my mouth without my hands if I have to and partly to keep it as tucked in as possible, to make it a less opportune target for a grab. That reg is on a 22" hose. It's not for anyone else.
Notwithstanding all that, you make some good points and it is rolling around in my head to go back to the other style of bungee necklace.