I wonder how much mouth damage from some of these rigs is down to bad unhooking?
I have no problems in cutting the hook, on the shank, just below the eye or as low as I can get, and then feeding the point through. The cut eye section will fall away with no problems. It is fiddling and faffing and forcing the hook free (with any rig) that can cause (additional) damage. Then dose up the hookmark, or marks with Klinik or similar hookpoint antiseptic treatment
I would much rather tie on a fresh hooklink, rig or hook, than expect to re-use the same one each time.
Please don't get me wrong, I am very tight on hooks, and materials, if it is sharp enough, then to me it is good enough, but for the sake of NOT damaging a fish, I would far rather cut the hook or hooklink than be responsible for mouth damage.
A good pair of wire/side cutters is an important item to have in the tackle box for that very reason.
I think that it is long shank hooks that can be the cause of much mouth damage, especially in small fish, whatever pattern, Carp-R-Us Longshank Nailer, Fox Series 5, Ritchie MacDonald Z13 or PiggyBacks, whenever there is a chance of double hooking, and I think that many anglers are using fashionable rigs, without necessarily knowing or being able to think out the potential risks. It is not even their fault, but since Rob Maylin first published the Bent Hook Rig, it got used everywhere, and the same is true of the 360 rig.