If you want to be able to do jumps like that, there is a class for it: monks.
The idea that every class should be able to copy or mirror everything another class can do bothers me. I don't want a homogenized game, and I don't want a D&D game where fighters are Goku.
Why shouldn't wizards be able to have 200 HP? Why shouldn't monks be able to wear plate mail? Why shouldn't rogues be able to make eight melee attacks in a single turn?
The ability to reach your opponents is a basic one, and no class should have to feel thankful because some high level ability "grants" them this ability at high level.
Every martial class needs to move about the battlefield, not just monks.
A fighter that can't actually reach the monster is useless. (Or drives everybody to ranged builds, which is not a great solution either)
So. Since the game makes it fairly cheap to get things like Misty Step, if you get your way and gatekeeps even the basic stuff from non-specialists... this simply means I will get hold of Misty Step (or similar) through a feat or some other source.
But that just means the notion that magic is the solution to everything gets entrenched. Much better is to be exceedingly generous in your interpretation of the core movement rules, and never bitch about one feet here or there. There is NO practical difference between being able to jump 16 or 18 feet. What the game asks you to do is jump 20, 30, 40 or even longer and higher. And if the movement rules won't let you do that, magic
easily does.
Remember, being able to jump 16 feet all day long is not
nearly as useful as being able to jump 60 feet once a day.
Since the end analysis is that any decently experienced player worth his salt will still get hold of the abilities he needs to reach the monster. Let the Rogue move (jump, climb) using Acrobatics. And let Athletics and Acrobatics
be actually impressive, commensurate with what a high level character should be able to do.
The idea that only Monks should be able to do that is deeply problematic.
The idea that Monks should be grateful simply because they can move is even more problematic.
The game is just way too easy to game here. Nobody plays a slow plate dwarf in 5E, when you can make other choices that does not compromise your damage output too much and gets you really useful movement capabilities.
Remember, any round that slow Dwarf doesn't reach the monster is a lost round. You are much better off being mobile. Even if your DPR is slightly lowered, actually being able to deliver your DPR is a fundamental key to creating an effective character.
Abilities like Misty Step are
soo useful. They're not needed in every fight, but they are likely a gamechanger (in the character's ability to actually dish out damage) in one fight every session.
Trying to restrict regular movement to some notion of real-life is just so very misguided, in the context of 5E. The
only thing that accomplishes is driving martials into the arms of magic abilities.
Conversely, allowing martials to perform actually awesome feats of movement doesn't impact balance nearly as much as you think, since decently minmaxed martials will move about at will anyway.
The only choice is between "magic is the solution to everything" and... allowing martials to be awesome without magic.
Monks get to be specialists in lots of ways, but don't even begin to think "actually reaching the monster" is something only Monks should be able to do, because that's just not the reality of the game.