Personally, when trying to decide between two different interpretations of the rules, one of which is narrower than the other, I think evidence of how the designers run their own games and the content of the official modules they approve is worth considering. That evidence isn't necessarily dispositive, but I think it can still be informative.
I mean, which is more likely? That the designers articulated a narrow standard of play, and then failed to adhere to that narrow standard in their own games and also routinely approved modules that failed to adhere to that narrow standard? Or that the designers articulated a broader standard of play, and the diversity of methods they use at their table and the modules they approve meet that broader standard?
There's room for debate, but personally I think the latter is significantly more likely. Under my interpretation of the climbing rules (that the rules leave it up to the DM to decide what qualifies as a climbing complication) it makes sense that the designers left such decisions up to the module writers.
(And yes, I suspect that the bias towards calling for checks in the modules stems from the writers of the modules being more familiar with previous editions. But since I read the rules as giving the writers discretion to identity climbing complications, I don't see the modules as rule violations even if I might question the writers' judgement on what checks to call for.)