iserith
Magic Wordsmith
The search function is not turning up the thread for me, but some time in 2018 (I think it was) there was an extensive thread about this very issue in which I believe you participated. Your reading of those rules is not the only one. In particular, some people - including regular 5e players - think that the reference under the Athletics skill entry (Basic PDF p 59) to "try[ing] to jump an unusually long distance" establishes a framework within which attempts to jump further than a PC's STR score might be resolved; and that the statement under the Movement heading (Basic PDF p 64) that "Your Strength determines how far you can jump" should be taken to be qualified with an adverb such as "usually" or "with certainty".
That's not entirely accurate. Strength(Athletics) allows PCs to try and jump an unusually long distance. It doesn't give how far and with what DCs, so one DM might be like for every 5 you get on the check, you go 1 extra foot, and another might be for each number higher than 15 you roll, you go 1 extra foot or a number of other methods.
You get to go your strength distance with no roll(certain). X extra feet possibly, depending on the roll and DM method(uncertain). And no roll if the distance is simply not possible with Strength + max X(certain).
An ability check doesn't allow the character to jump an unusually long distance. An ability check doesn't exist in the fiction. A request to make an ability check is not an action declaration. A task of some kind that is performed by the character (which the rules do not specify and must be described by the player and judged by the DM i.e. the "special circumstance" I mentioned in the post you both quoted) might allow for a character to jump an unusually long distance and a Strength (Athletics) check may be appropriate if the outcome of that task is uncertain and there is a meaningful consequence for failure. As with all other actions the players describe, including whether or not a Charisma check resolves an interaction with a baron, the DM still gets to decide what happens.