I suspect those tethers are there for the same reason as mine.
My tether is about 10 ft and I use it to secure the anchor
in the rollers. Having it permanently on the anchor
reminds me to use it, and its right there when I want it.
A long, long time ago, in heavy seas, my anchor jumped out of the roller and pulled out a lot of chain before being stopped by a chain "knot". Otherwise all 250ft of chain could have run out. It was noisy and I hadn't heard anything but had this funny
feeling that something was wrong. I hove to and went forward. It was night, I was single
handed and, had I not been in deep water
... need I say more?
After everything was sorted, a quiet word with my Friend was in order.
Since then, I always, always used an anchor tether.