The Crimson Binome
Hero
The entry gives examples, which the DM can use as basis for their adjudication. I would definitely say that a free-standing rope with zero support is the equivalent of a steep cliff, since it is purely vertical and there is no wall to lean against, and there are no easy hand-holds.The Athletics entry (p. 175 PHB) makes it quite clear what climbs call for an ability check. It does not include a free-standing rope.
The basic rule of the game is that the DM calls for a check whenever the outcome is uncertain, and failure would matter. Since I can't state with 100% certainty that absolutely anyone would be able to climb a free-standing rope with 100% success rate, and since failure would cost time in a situation where individual rounds would matter, I am confident in adjudicating that a check is appropriate in this circumstance. And to be perfectly honest, I don't see how you could seriously propose otherwise.