Imo mouth damage through weed fishing is caused by inexperienced anglers trying to drag them through it, particularly with braid. I have never seen a fish tethered in weed. Imo they just use it to their advantage. Hence when you lose a fish (in the weed) it's always easy to retrieve the rig. In my book as long as the rod is locked up in weed, the fish is still on, otherwise it just pulls through. It can be a very long and arduous task extracting them without a boat and without damaging the mouth.
That's just my observations of course.
Most jetties were built for either boats or for match anglers as a peg and in many cases they were built before carp angling was mainstream. I'm sure most waters that are built as carp lakes nowadays would consider building them big enough for shelters.