So you want a superhero? I don't want superhero fighters. I don't want them lifting tons. If I wanted to play a superhero, I'd play a superhero game.
First off, these would be talents for a brand new martial class, not the fighter. The fighter can remain completely mundane for people like you who don't want fighters being similar to warriors from myth and legend. Secondly, you don't even have to choose the talents that make you "superheroic". Since the talents would be a list of options (similar to warlock invocstions), you can simply skip over any option that offends your delicate sensibilities.
Also how do these talents even make you "superheroic" in the first place. Do you think 4x your carrying capacity somehow makes you superheroic? That only brings your max carrying capacity to only 1,200 lbs. That is miles behind the likes of actual superheroes. Hell that is still way behind the likes of heroes like Lancelot (the strength of 10 men), let alone Hercules, Beowulf, Gilgamesh, CuCuchlain, and others that are given as examples of high level fighters in 2e.
If jumping 2x as far as normal seems superheroic to you, I should probably introduce you to an at-will warlock invocation that allows them to jump 3x as far as normal. Is the warlock also superheroic?
Besides, if you really want to play a super hero, you play a spellcaster. Everyone knows that! They have capabilities that would put even the most powerful superheroes to shame.
you want the ability to build a charisma-based fighter? You can the charisma stuff multiclassing. Why would you need to lump it all under the fighter?
Sure, I guess multiclassing could also work. 1 level of mystic gives you advantage on all Charisma checks, which is better than the two talents I proposed. Multiclassing rogue gives you expertise (among other benefits), which is also probably better overall for non combat utility. And sure, a spellcaster could make use of cause fear, charm, command, suggestion, dominate, and the like to be much better at interaction encounters. But why should you have to multiclass?
Why can't there be room for a persuasive or intimidating purely martial warrior? That archetype is common throughout fantasy. Why can't there exist a martial class that is actually decent at representing the typical martial warriors from fantasy media? And what if multiclassing doesn't fit your character concept at all? Lots of classes come with large amounts of baggage attached to them that makes multiclassing not always ideal. Some people don't want spells, or sneak attack, or psionics, or any number of features that clash with their concept. Why should they have to multiclass just because they want a non magical martial warrior with a small amount of non combat utility?