Fair enough. Be that as it may, I think we can all agree that by raw, a check is not enforced for something like climbing a tall rope, or a stressful drop.
I definitely think that we can all agree that the DM is not required to call for a check. The disagreement is on whether the DM can choose to call for a check if they identify a climbing complication, or whether only certain types of climbing complications are allowed.
And I presume we can also agree that 5e design philosophy is in favor of simplicity and a lot less rolls.
I agree on the simplicity and being written to
allow fewer rolls. But it certainly seems to me to be set up to permit frequent rolls, if desired. As evidence I would point to DMG 236, that discuss the style of calling for lots of rolls and discusses the advantages and disadvantages of doing so in comparison to other styles. The text does not suggest that any of the discussed styles are favored or disfavored in 5e.
So our interpretation of the rules is at the very least in line with that design philosophy. And that is something I've been trying to get at the last few pages. There's not just the rules as written, but also 5e design intent that supports our position. After all, climbing, swimming and jumping were made into movement for a reason.
I entirely agree that your interpretation is in line with the design philosophy of 5e. I just also think that other interpretations are equally in line with the design philosophies of 5e.
On your final claim, however, I have a quibble: the rules state how much movement climbing, swimming, and jumping consume. They don't say you can use those ratios to convert daily land travel distances into daily climbing, swimming, and jumping distances. Merely providing a ratio does not otherwise suggest an equivalency between movement types.
There simply seems to be a lot of resistance to 5e's style of play. Its simplicity, its handwaving of rolls, and its focus on expediance. But these are the strength of the system in my view. They are what make 5e different from older editions. 5e is more than just a rules-light version of 3rd edition. There is a different mindset in 5e in regards to how D&D is to be played. And it has honestly changed how I run older editions as well.
It is to be embraced, not resisted. And I know that may sound odd coming from someone who prefers 3.5. But I do get it, and I appreciate what 5e is trying to do. We shouldn't look back all the time. We should also look forward, and recognize that a lot of this handwaving is an improvement, and the new way of playing D&D.
From my standpoint, one of 5e's largest strengths is its ability to support play in multiple playstyles. I wish it was even better at doing so, but by my reading the purpose of the simplicity is to give DM's flexibility, not to try to imply a specific, restricted "mindset" of play.