If I may add....
I've seen a fair few arguments 'for' and 'against' the use of barbless hooks over the years, but I don't think one of them has really ever looked it from a balanced point of view. Not one has considered how fish are never hooked in exactly the same place (possible with certain techniques, but not hard baits and trebles) or really put the theory directly against the fishing the writer is doing. I'm not saying I'm trying to do that (I don't know enough), but to look at it from both sides...
I coarse fished for years, and from almost the beginning barbless hooks were common. Initially just for quicker unhooking in match situations with small fish, but eventually the majority believed that they have superior hooking power and also holding power. To a degree, the same can be said in lure fishing, but it's not clear cut.
Barbless hooks (like the author of the above article says) give a smoother, deeper penetration in to a fishes flesh. In a carp situation I think this is pretty much be written as gospel - although some fishery owners will still argue to opposite to be true and actually ban barbless hooks! Carp (specimen or match) fishing requires techniques that almost certainly ensure the bait and the hook are INSIDE the fishes mouth when it is hooked. With the barbless hook holding a good position inside the mouth, hook shape can play a big part in ensuring that the hook moves as little as possible during the fight, and stays put, deep and strong. Even slack line will not guarentee that the hook will come out! In fact, slack line will rarely make any difference to a barbless hook if it is in the right place (i.e. inside the mouth).
Our sea fishing is slightly different, but the same principles do apply - they just need to be tweaked a bit I think? Current (single) hook shapes probably don't lend themselves to barbless points since they won't have the same bends to maintain that hold - so keeping a taut line becomes more important to ensure the hook doesn't slip. Still, as has been said, rarely in a fight will the line be slack unless you make a mistake. Traditional sea angling, waiting for predominantly small fish to hook themselves against ounces of lead doesn't lend itself to barbless hooks. The smaller the fish are, the harder barbless hooks are to use successfully. To fly in the face of tradition though, the techniques could be adjusted to allow it to happen - and probably adjusted in a good direction too, success and efficiency wise. That would be a long way off though, but I believe that a freshwater influence on rigs could prove huge in the longrun.
Treble hooks, with shorter shanks than most single hooks, are part way to providing a better hold (on a barbless point). A rounder point will also help (think circle hook almost). Any one of the average 6 points on a lure hooked INSIDE a fishes mouth is likely to provide more than enough holding power for you to land 99% of bass you hook. Again, even slack line will probably not be enough to lose it for you if it's hooked INSIDE the mouth.
One inconclusive side to the argument is how much damage each type of hook causes to the fish. I'm on the side of the barbless, but again depending on exactly where the fish is hooked, some argue that barbed hooks - when they move during the fight - will turn and cut/loosen the flesh around the hook hold. If a barbless hook turns on the spot however, the hook hold stays round and strong with no loosening of the surrounding flesh - which is why the previous slack line mention holds true. I'll repeat - this depends on exactly where the fish is hooked, but assumes deeper flesh INSIDE the mouth. Whether the hook twisting/flesh loosening theory is correct though, I don't know. I don't know whether anybody can really give a factual answer yet.
However, not all fish are hooked perfectly inside the mouth in a deep enough piece of flesh for all of the barbless arguments to hold true. I could run through each part of a fishes head and suggest why or why not a hook of either type might loose its hold, but I'd be here all day. Basically, this is where I don't think its quite so easy as saying yes or no to either type. There's almost like a middle ground where a barbed hook probably IS more likely to land you a fish should something out of the ordinary happened. I probably shouldn't be preaching this since I still lack the confidence in my lure fishing to actually be 100% barbless yet, but we probably shouldn't fish expecting the worst to happen. It rarely does, its just unfortunate that we remember these times the most vividly. Either side of that middle ground are the areas where barbless hooks, in theory, should actually be better - and not just for easier unhooking. You could almost look at like barbless hooks winning 2-1.
I've used barbless hooks with 100% confidence for large and small fish in coarse fishing situations for years, so should sort myself out with the sea side of things now really. My head says one thing, but the 33% uncertainty has prevented the move so far - like it has for most people I'd imagine.
What needs to happen is for hook manufacturers to start coming up with more features on their barbless hooks to promote stronger hook holds. As I mentioned previously, barbless hooks of the right shape will not slip so much, and this is most people's concern with going barbless. "I don't want my 10lb bass to come off"...... "it won't, mate" (at least if it's hooked properly) ....... but there's no way most people would blame it on anything other than the barbless hook. If a big 'point' was made by the manufacturers and the right anglers, we'd all be barbless inside 2 years.