Here's another viewpoint I got from my more wise and experienced partner in a recent one-fly tourney. I was doing the river fencing bit and changing the direction of pull to try to disorient the fish. My partner pointed out that every time I did that the hook was "wallering out" a bigger hole and making it easier for the fish to get the hook out. This made perfect sense to me!

I suppose this might not matter on a fish caught on a bigger hook or with an especially rubbery mouth. However with my size 16 soft-hackle on 14" rainbows, holding the rod more still seemed to cause fewer fish to get off.

Thanks to Judd from Monroe, LA for clueing me into this!