You don't feel your player whose character has broken hands might anticipate difficulty climbing? As a DM, you can't go outside the bounds of examples in the book? They're limits, not guides?
Again: in the end, it's up to the DM and, of course, the examples are not exhaustive. Of course the examples are guides. You don't seem to like that answer that has been given over and over - the examples are indicative of difficulties introduced to a climb/swim that would required a Strength(Athletics) check. Length of swim/climb is NOT in the same category of difficulty. Asking the same question over and over is not going to get you a different answer on this. Do you have something specific you are trying to conclude here?
In your example, the PC has broken hands. Climbing with such a condition is not a matter of Strength but of grit, determination, and/or pain tolerance. I'd might rule they can't even climb at all. OR, I might rule that they'd be slower climbing AND if some external difficulty came up, they'd have disadvantage on any roll to keep making progress. AND/OR, I might require a CON check/save to overcome the physical pain involved to climb with broken hands.
The guidance provided in the books, however, does
not encourage a DM to call for a Strength(Athletics) check just because someone is attempting to climb or swim
with no other external difficulties introduced. I mean, absence of an example doesn't 100% prove anything, however, it would have been sooooo easy for the designers to say: "At the DM's option, if a climb/swim is excessively long, a Strength(Athletics) check might be called for." (Or whatever such wording that doesn't end in a preposition.) What they do say is that an excessively long swim might require a Constitution check or save. Note that they do NOT explicitly say "instead of a Strength check/save". The books is
not suggesting we swap Con for Str here. A different question is being asked: does the PC have the stamina to keep going? QED, it is not supported by the specific rules in the case of a very long swim/climb to call for a Strength(Athletics) check if no external difficulties are involved. I'll repeat my caveat since some folks (not you
@clearstream - I feel like you are trying to engage in thoughtful inquiry) like to harp on it and will somehow forget that I led off with it: at any given table, it's ultimately the DMs call because... rulings not rules.