For clarity, are you arguing that "climbing a slippery vertical surface" or "[a surface] with few handholds" are the only two types of complications for which a DM has the option of requiring a successful Strength (Athletics) check to climb?
No, he's arguing 'climbing a knotted rope with a wall to brace on' is not in the same category as 'climbing a slippery vertical surface' or 'climbing a surface with few handholds'.
Climbing (by default)
does not require an ability check. It only requires a check when there is a reasonable prospect of failure (akin to trying to scale a sheer, vertical and slippery surface, or one with no handholds.
A knotted rope is neither of those things. It is not slippery, and has handholds (and footholds) the whole way up.
Secondary sources such as modules that have specific call outs for Climbing (LMoP) that give DC's for the Climb also expressly state if you have a rope, you dont need to make a check at all. Prior editions of the game (and related games like SWSE) more or less make climbing a rope with a wall to brace on automatic as well.
So far in this thread I've seen people argue for a DC from 8-15 to
climb a knotted rope, including calls for checks every single round worth (15') of progress, with failure meaning falling off the wall, meaning no sane healthy adult (Commoner, Str 10, 4 HP) would ever attempt a rope climb, ladders and trees are the things of nightmares, and actual mountaineering is a death sentence.
I literally cant understand how people can even call for a check to climb a rope, let alone set such an insanely high DC.
I get that most of us are likely nerds who likely struggled in gym class as kids, but come on.