I would draw your attention to the text "
Examples include the following activities:"
@6ENow! makes a similar point. "
Your Strength (Athletics) check covers difficult situations you encounter while climbing" for them, a lengthy climb is in itself a difficult situation. The absence of an example does not rule it out. The general rule is that "
The DM calls for an ability check when a character or monster attempts an action (other than an attack) that has a chance of failure."
One of the most important pieces of guidance is "
Together, the DM and the players create an exciting story of bold adventurers who confront deadly perils." If a group find it exciting to have a chance to fall from a lengthy climb - where the only challenge is the length of the climb itself - then I believe they are robustly supported in the RAW for deciding to do exactly that.