For his study, graduate student Chris Pullen used four identical lures and embedded the hooks in different areas in the pike's mouth. He also placed trackers in the lures so they would know exactly when, or if, the fish shook the hook out The results were pretty surprising.
All four baits came out of all four test study northerns fairly quickly. Pike were hooked in the lower jaw with both barbed and barbless hook as well as through both the upper and lower jaw. Finally, one was hooked deep in the mouth, as often is the case when a northern inhales a lure.
The baits with pinched barbs came out within 24 hours. Surprisingly, the deep-set hooks actually came out quicker than the baits hooked in the jaws with barbs. The test assumed the baits on the jaws didn't affect the pike as much as the bait set farther back in the mouth. So it didn't work as hard to get them out.
Overall, what this test shows is it's probably better to just cut the fish hooks farther back in the fish's mouth than to dig them out with pliers. If a northern does break you off, chances are it'll kick that bait in short order. Then it'll probably go on to break somebody else off.
We're guessing the results of this test would be very similar for muskie. We need more tests to confirm if this is the case for all fish or just for freshwater fishing. It doesn't appear someone has done a similar study for saltwater fishing yet. It would probably be worth looking into considering how many saltwater species anglers cut or break off on purpose near the boat. That method is generally accepted as a form of catch and release. It would be helpful to know if those treble hooks left in the jaws are either shook or later dissolved by the salt water. However, a least of this particular culprit, it's good to know most survive the encounter after a hook set.