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Haven't seen the hand reel that launched this thread, but have done a lot of hand line fishing, and so have used hand reels a lot. Wrapping it by one hand "walking" sounds inefficient compared to just holding the "reel" in one hand and wrapping line on it with the other, but as said, I haven't seen this one.
Also, it is usually inefficient to put hand line back on a reel as you bring in a fish and doing that will cost you some fish, unless they are very small. (I hand line in the ocean mostly, big fish). As you pull line in, just drop it in the bottom of your canoe or on the (uncluttered) deck of your kayak. If the fish runs, let him go. He can pull out the naturally coiled line without tangle. With line on a hand reel, he will be snubbed up solid, and usually something breaks or tears out.
A rod allows us to use light line because the tip flexes and cushions any hard pull on the line, rather than snubbing it up hard with no give. I have hand lined fished for trout through the ice (rainbows to ten lbs.) and you simply have to go to heavier line or you break it off when the fish darts a run and your hand doesn't give with enough quickness and finesse.
Also, as said, light line cuts into your hand.
Hand line in Pacific coastal waters usually runs 200-300 lb. test mono, not so much for strength as for ease on hands when handling fish of 20 lbs or more.
A board the size of a cedar shake, with a deep notch in each end makes a good hand line holder. The best, as I posted in another thread, is an Australian hand reel. It is shaped like a plastic doughnut a foot or larger in diameter, with a flanged rim that holds the line as you wrap it on. It is sort of like a giant open faced spinning reel, so that line comes off a lower rim or lip on one side of the flanged reel. It has a cross member across the middle of the doughnut, to hold in your hand.