This appears to be a matter of implementation rather than an absolute problem.
I assumed everything in this thread is a matter of implentation or degree, and nothing or very little is an absolute problem (although the "furries" seems to come to close) although some seem to frame it that way in black-and-whites.
If, for instance, a fighter gained 20% (compound) to his leap distance each level would you have a problem? He's always been good but it's hard to nail down exactly when he blew the curve and kept going.
I'm OK with any mechanics that encourages the range of human expression or behavior that is consistent with the underlying fiction.
So as we talked about upthread, a fighter points pool or something is fine. Maybe leaping 500 ft once causes fatigue and you could leap again but you'd suffer a disadvantage. I don't know, just anything other than a mechanical fixation on 1 x day and binary on|off toggles. I'd like to see why a fighter could smash a mountain but not save that potential to smash a villian dead in a boss fight, not just as a mechanical problem of nova'ing and separating combat vs exploration pillars, but how is that differentiated in the fiction: what is the fighter thinking/doing?
The result may not be a perfect match, and that's OK because that's historically forgivable in D&D, but really any honest attempt at doing so is integral to a unifying solution IMO.
Again though, it depends on the fiction. Say a fighter gets a mythical fey boon "You may leap to impossible heights". The fighter, previously capable of Batman-like athletics but unable to jump supernaturally, is now suddenly but plausibly able to jump 500 ft. The fighter still can't do other supernatural athletic feats, like hold their breath for 7 days or smash mountains or whatever, and that's plausible too because the fey boon was very specific.
Anyway, this fighter jumps 500 ft once, and then wanders off to the base of a cliff that he wants to scale to get to the mysterious keep at the top, but he can't leap it to it the 2nd time. He only leaps the usual extraordinary but otherwise mundane height. The fighter probably feels confused and cheated (as any real person would, unless we're roleplaying the fighter in less immersive ways).
So the fighter goes back to the faerie patron and demands an explanation. The reply is "Aah, silly mortal, the magick is like a fruit, once eaten, it is gone, and only replenishes at dawn" (or whatever).
So the fighter goes back to the cliff, decides if he wants to go to the long way round, scale the cliff the hard way, or maybe just camp for the night and wait until dawn to leap the easy, magical way.
And maybe that fighter, when he feels up to the task (ie. higher level), goes back to the faerie creature and threatens to bash its head in unless the faery grants him another boon or maybe stronger magick so he can leap thrice a day or whatever.
That's just an example from the top of my head. The point is for me, the explanation (which is supposedly just fluff according to some people or irrelevant or not needed) is not just a side thought for me, but part of the foundation for the mythic mechanics at its inception.
Edit: removed the reference to testing the 1st jump