Hilarious. I seem to hold on to my rod if I fall in the water or out of a canoe into the water. But on dry land, I always let go and have often wondered if I should hold on to the rod.
You should try bushwacking British Columbia's coastal steelhead streams in the steeper parts. Falling is the norm. If lucky, the rod lands on soft moss or is gently supported by a thicket of Devil's Club. You may end up picking Devil's Club spines out of your skin for several days but as long as none of the equipment breaks, all is good.
Walking across bars of head-sized rocks is always good fun too.
FWIW, I like the Simms G3 Guide boots with the Vibram rubber sole for hiking. (Felt is awful if not downright dangerous for hiking.) Aluminium pucks screwed into the bottom of the rubber outer sole take care of the traction on slippery rocks.
Science is not common sense. Much of it is devoted to a systematic documentation of what we do not know and understand.