Ok, I just want to thank everyone for their civil debates about the rules (and rulings) in the situations of special movement.
I will conclude (yes, I
really am done this time LOL

) with the following:
Following the RAW allows for the DM to ask for check under special circumstances, which IMO includes height and distance for certain movements. The DCs would likely be low in most cases, but they would be there. To not ask for those checks reduces those "challenges" to narration, which removes them pretty much IMO. In the case of the OP, simply having two lengths of rope and a grappling hook is all you need to overcome the challenge--no check required according to some here. Which means no challenge unless you want to add another factor. There is nothing wrong with just making such things narratives, but it isn't for me, personally.
Also, many posters complain about the lack of exploration challenges in 5E. You are basically shooting yourselves in the foot if you don't call for checks due to more mundane complications like height or distance. Consider a party who reaches a lake 5 miles wide but 100 miles long. It will take them days to go around, but according to the RAW they can all just swim across in a long day of leisurely swimming without the need for a check.
Yes, I KNOW I can add elements to make this more "exciting", etc.; that is not the point. The point is the lake should be an obstacle IMO. Crafting a boat or raft, etc., finding some way to cross because realistically your STR 8 gnome sorcerer without athletics proficiency would likely drown otherwise, is the challenge.
So, if the PCs insist on swimming, I will call for a check because of the grueling ordeal they are attempting and drowning is a real risk to them.
If you just let them cross or handwave it away, you are removing the obstacle for them. Yes, you can throw in something more, but I don't want every encounter of such obstacles to need tension in addition to the tension and challenge that those obstacles already present IMO.
A PC with sufficient skill/modifier would auto-succeed, sure. Now, we
do house-rule a 1 always fails ability checks and a 20 always succeeds (and the same for saves).
THAT is a house-rule and I get it. But choosing to accept that height or distance can fall within the realm of presenting significant challenge in a manner similar to the examples provided is part of "At the DM's option" and also falls within the RAW.
If you don't agree with that, fine, but don't tell me I am "wrong" or "not following the rules", because I am not wrong and I am following the rules as our groups interpret them.
If you want to more strictly judge those conditions that would call for a check, that is your choice and I will never say you are wrong for choosing to run your game your way.
At any rate, thank you again, and I am praying this thread does not come to rival why "we have gnomes and halflings". Cheers.