A trout's brain is very small. It is sometimes said that dry-fly fishermen "pit their brains against those of the trout". No-one has ever leveled a bigger insult at us. Dermot Wilson - Fishing The Dry Fly
This past season I guided two anglers who took too long to land a trout. Both hooked a trout and then began to lower their rod off to the side, one side and then the other. The trout swam around at will and after what seems FOREVER the fish came to the net. A third angler did the same but lost the trout and fly and tippet to a sunken Millers dead fall. That's what happens when you play with your fish instead of PLAYING your fish!!
I haven't a clue how this weird technique metastasized but it is totally unnecessary. Your goal it to bring the trout to the net as quickly as you can without breaking the tippet if you really believe in proper catch and release.
Let's say you hook a trout. It's first action will be to move AWAY from the PULL that you induce and to go deep. FORCE THE TROUT TO THE SURFACE where it doesn't want to be. It will begin thrashing about and EXPEND far more energy than letting it swim around at will. USE YOUR ROD to make this happen. Don't bend your rod into a candy cane shape but raise your rod arm enough to make the rod bend from the tip into the mid section of the butt. Your rod, acting like a fulcrum, will flex to every surge the trout attempts and it will be like a weight being pulled. Maybe your reel and it's drag system might even get into play. Get that fish thrashing up on the surface, in that half water, half air zone and it will tire quickly. You will net it, take a quick photo WITHOUT YOUR MITTS ON THE FISH, and then release it.