I had the same problem before but on another type of vehicle, and like
@Blue Ox would stomp on it to get it to free up. It was so weird because the cable seemed fine and like you all, would unhook it and it was smooth as silk, but hook it back up and it would hang. I think it turned out that it wasn't the cable but something was wrong with the carb linkage. Cleaned the carb real well and it freed up but never did actually know what it was, but it didn't happen again so I forgot about it.
Then when the truck I have now had a 2 bbl. on it it would hang up from time to time and I would have to tap it pretty good to get it to release similar to my other car. And like you all, unhooked the cable and it was smooth, etc.. But I never did replace the cable. Just cleaning the carb seemed to do the trick.
So if it's smooth when it's unhooked but hangs when it's attached to the carb linkage, what is causing it? I to have seen those cars with the hard plastic cable housing made all curled in a S shape. Doesn't GM know it's going to wear inside the housing and cause the cable to hang eventually? Hey, I like the carb linkage that is a metal lever that is connected directly to the foot pedal and up to a short piece of cable going to the carb, like the early Chevy's are, ha, ha, ha. It can't hang if there's no fancy cable and plastic housings and what not.