Historically, fighters have prospered by finding magical Boots of Jumping, not by developing spontaneous superpowers that allow them to jump like Spider-Man while naked. Do you hate magic items? Well, I can understand that. I kind of hate them myself. But I hate D&D: X-Men even more.
D&D is a game where, outside of binary gravity and HP, almost everything weird and fantastic that happens has to be explained by magic. Your magical Jumping Fighter can now be modeled as an Eldritch Knight who learns the Jump spell, or a regular fighter who multiclasses to wizard. You don't have to learn magic, but if you don't, you won't be doing magical things while naked, so you better stock up on magical items, give up on super-jumping, or persuade your DM to house-rule 5E until it's more like Marvel Super Heroes or Feng Shui.