(Emphasis added.) This is the same type of philosophical difference I was discussing with @Charlaquin earlier in the thread. To me, the bolded passages are in conflict. In the first one you're saying the rules leave the decision up to the DM, but in the second you're using your own judgement of designer intent to say that a DM who uses height of the climb as a climbing complication isn't acting within the rules. To me, that sounds like you're saying that, to be acting within the rules, a DM must only choose complications that you believe are line with designer intent, rather than what that DM believes are in line with designer intent.According to the rules, the DM decides if a complication makes the outcome of the action in doubt. Examples of complications are given. Height of climb, or scaryness of jump are not examples and do not seem in line with designer intent.
However, the rules are but guidelines. The DM is allowed to make their own calls on the matter. But to reitterate, this is not a discussion on whether the DM is allowed to make such calls.
Broadly speaking, I think this comes down to fundamentally incompatible ideas of what "correctness" means. You're comfortable with the idea that the rules both give decision-making authority to identify climbing complications to the DM, and simultaneously expect that DM to "correctly" determine which complications are of a type with the examples in the book. From my perspective, "correctly" determining which complications are of a type of with the examples in the book is, in practical terms, meaningless without some standard for gauging similarity. And if that standard is anything other than "whatever that DM thinks is similar" then identifying complications was never up to the DM in the first place--instead it was up to whomever designed the standard for similarity.
Even more abstractly, I get the sense that you (and other posters arguing similar positions) are concerned with the question "What is correct?" while I am concerned with the question "Who decides what is correct?" That's probably why you're (apparently) more willing to dismiss my interpretations of the rules as incorrect, whereas I'm arguing for the validity of both interpretations and merely expressing which one I think is stronger. It's probably also why I also react negatively to posters arguing that their interpretation is correct and mine is wrong, because I'm interpreting such an argument as those posters implicitly claiming the right for themselves to decide what is and is not the correct interpretation of the text.