Have you ever watched Deadliest Catch? Things like that happen so fast there is almost no time to react. It’s also likely that he may have been knocked unconscious by getting slammed into the rail as the pot dragged him over the side.
So you are under water and you pull your knife and cut the rope.
I used to serve in a military unit that tested us by blind folding us while we were fully armed and dressed, and having us walk into water, the test was to simulate patrolling in pitch dark and then suddenly finding yourself in a river or pond, a person merely lets things settle down for a second and then deals with the situation.
While you guys are arguing against a knife being helpful, I personally would have had a knife, I carry two on me everyday just living regular life, and would sure have had one appropriate to doing that work.