Funny you mention that - the first time I heard of the bungee was for the spinnaker, and I had never seen an instance where it was needed and never had used it. But then I learned...
In theory, my trap handles have constant tension too, but a combination of lowering them a bit and re-using some older bungee resulted in the sag. As mentioned above they got caught by the spreader during the tack. When the crew went out on the wire, the load was enough to pull the mast rotation back a bit and suddenly release the captured tack line resulting in the shock load as the crew 'fell' a few inches. This ruined a good regatta for me a couple summers ago as my crew went for a swim which is decidedly not fast. Tried to do an on-the-course repair, but spectra/dyneema doesn't like knots (too slippery) resulting in a second swim.
Now I try to keep a bit more tension on them, run the above-mentioned bungee, and have a reserve trap line setup on the boat in case the poop hits the air-mover.