Jumping. I want to focus on just jumping for a second, and how this can help formulate designing a mundane high-level fighter.
In real life, the record for a non-pole running high jump is 2.45 m (or 8 ft and 1/2 in) set by Javier Sotomayor (Cuba) on 27th July, 1993. (source:
High Jump World Records) This is measured from starting position of the feet to ending position of the feet, so it's very precise/clinical, and doesn't account for adventuring scenes where you're reaching to grab something, but it's a starting point.
In current 5e D&D you can running high jump up to 3 + your Strength modifier. And with ability scores capping at 20 (+5), that puts the maximum mortal running high jump at about Sotomayor's accomplishment – 8 feet.
Compare that to a Strength 10 (+0) character enchanted by the 1st-level
Jump spell (the creature's jump distance is tripled for 1 minute), and that average character is running high jumping 9 feet – exceeding what the best fighter can do! Geez!
No feats increase high jump AFAIK & Champion's remarkable athlete only applies to long jump. OK. So "take existing feat/subclass" counterarguments don't apply.
So if we imagine that a high-level mundane fighter should at least be high-jumping MORE than what an average strength character could with
Jump spell – which seems to me like a very modest to low bar to start with – how do we design this?
There are two big categories that we can approach it from: (1) Hard number design (which 5e favors for jumping), and (2) Soft narrative design (which is generally more "indie" and disfavored in mainstream 5e). So I'm going to proceed with #1 assuming that will be most accessible to the most number of folks...
Jumping high doesn't seem like something that should be EXCLUSIVELY high level, but it does seem like something that should be BETTER at high level. So maybe using Proficiency Bonus as built-in scaling mechanism would be a solution?
Whenever a fighter makes a jump, they add their Proficiency Bonus in feet to the total distance jumped.
So a Strength 18 (+4) fighter makes a running high jump at 1st level (+2 prof), and they are reaching 9 feet – exceeding what Sotomayor accomplished and equal to what an average strength character achieves with a
Jump spell. That seems reasonable...
Then the fighter, now Strength 20 (+5) makes a running high jump at 13th level (+5 prof), and they are reaching 13 feet! An incredible distance! In some buildings this might be a leap up into the rafters to engage in swashbuckling swordplay. Narratively, it could either be described many ways - sheer superhuman strength, parkour running up/pushing off a post, assisting the jump with a sword or staff, performing a rapid muscle-up, etc. There are still ways to narrate it within the bounds of human potential.
For me, the problem here is the change feels microtransactional – it's this itty bit of design for one area of the game that is isolated from everything else. That is the kind of design 5e favors though. For example, this doesn't allow a 5th+ level fighter to reach the cloud giant's castle in the sky, whereas the 5th level wizard is dropping
Fly to reach it - this is a drawback of "hard numbers" microtransactional design, because in a more narrative solution the fighter might spend a resource point (e.g. Hit Die or "Mettle" pool) to explain how they reached the cloud castle.