The Hulk is a superhero. The wizard is not a superhero. He is governed by the mechanics of his race. He abides by the laws and limitations of magic. Giving a D&D character superhero powers means you move the game to mythical or supernatural proportions - definitely not centred around medieval Europe (perhaps Ancient Europe).
I feel compelled to respond to this - it's really and truly baffling to me.
You define being able to jump a long distance as 'superhero powers' when the Fighter does it.
But you believe that the Wizard - who can:
- fly
- teleport
- stop time
- turn invisible
- alter reality with a wish
- read minds
- enlarge or shrink themselves
- walk on walls
- turn into gas
- breathe underwater
- summon up eldritch beings and bind them to her will
- turn people into animals
- animate objects
- control the weather
- cause earthquakes
- travel to different planes
- mind control people
- kill with a word
- call meteors down out of the sky
...does not have superhero powers, because she abides by the laws and limitations of magic. Those laws and limitations, insofar as they exist, are not immutable facts of life; they're the game rules. They're same things that people are suggesting be changed to allow the Fighter to have more versatile and impactful abilities.
You believe that a Fighter able to jump further than any real human being is a superhero, and can single-handedly 'move the game to mythical or supernatural proportions'.
You believe that a game in which Wizards are doing the things I listed above - or even if we bring the scale down and say in which a Wizard is casting a fireball at an orc - or even if we take Wizards out of the equation entirely and have a party comprised entirely of Fighters - is not mythical or supernatural.
Mike Mearls himself has stated outright that The Fighter Exists in a World of Myth, Fantasy, and Legend. Dragons, orcs etc simply did not exist in Medieval (or indeed Ancient) Europe.
D&D is not only both mythical and supernatural in scope and content from top to bottom, it allows spellcasters to become far more powerful than any character of myth or legend.
Consider Odin. Not just a god, but
the Allfather of the gods - chief among them, and ruler of Asgard. In the Ljóðatal he enumerates 18 charms that he knows. Consider how many of them are easily and directly reproduced by spells - charming maidens (charm person), bursting free of bonds (freedom of movement), speaking to the dead (speak with dead), controlling the weather (control weather), etc. Consider how far beyond these a D&D caster's abilities go.
Consider that in the same branch of mythology we have Beowulf, who was specifically cited by Mike Mearls in the Fighter Design Goals article as one of the inspirations for the 5e Fighter.
Beowulf takes part in a swimming race - across a sea, fully armed and armoured, for 5 days and 5 nights - during which he kills 9 sea monsters. Beowulf deliberately fights the monster Grendel unarmed and unarmoured - to be fair, as the monster does not have either. When Beowulf grabs his arm, Grendel is terrified - he's never met anyone so strong. Beowulf proceeds to tear it off entirely, as we all know. Later, he holds his breath for an entire day when swimming to the bottom of the lake to fight Grendel's mother. He wields an enormous sword from the age of giants to kill her. He swims across another sea while carrying 30 suits of armour. When he fights the Dragon, his sword breaks on its skin, and the narrator informs us that it's Beowulf's fate for edged weapons to serve him poorly -
he is too strong, and they break when he hits things with them.
And yet here we are, with a Fighter who jumps a maximum of 5 feet further than a non-Fighter of the same strength. A Fighter who has to take a feat to gain proficiency with unarmed attacks, and deals d4 damage with them even if she does. A Fighter who can, at his utmost, absolute peak strength - lift half as much weight as the current real world record.