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From what I gather noodlers can get into places you're not likely going to get your bait into with a rod and reel. For example, many of the online videos show them submerged under log jams or under rock overhangs. In some of the videos they say that they can feel the fish before they are actually able to pull them out. This also makes me believe that these fish wouldn't be to aggressive going after any bait that isn't right in front of them. For some, I guess the benefits outweigh the potential dangers, or perhaps it's just the thrill of catching the fish in their own domain.
For adventure seekers, catching a big catfish with a rod and reel may not get the adrenaline flowing as wrestling a 100 lb (45 kg) catfish in its native environment with the possibility of losing that match and drowning.
That, and have you seen the price of heavy duty fishing tackle these days? ;-)