How do you think the fighter should have that comparable impact?
Mighty Deeds. Not something they get access to instantly, something they grow into. A Mighty Deed at (say) 5th level might be holding up the portcullis so all your friends can get out safely, then slipping under yourself. Something no living human on Earth could do, but which is only the teeniest, tiniest bit outside the realm of what ordinary Earth humans could do. It's something Conan could probably do, and something John Carter of Mars could almost certainly do
on Mars, because his Earth-trained muscles make him superhuman in Mars' lighter gravity. (Naturally that's not
really how lower planetary gravity works...but I don't see people tearing into Mr. Burroughs for the unrealism there.) Chokeslamming dragons and flinging an ogre across the room, tearing open steel gates with you bare hands. Stuff that is still extremely grounded, just probably a bit beyond what is 100% unequivocally achievable by merely well-trained fit humans IRL.
Around 10th level, things like what Beowulf describes, swimming for literal days
in full armor, AFTER having just fought a long, pitched battle. Things that are genuinely just impossible in our universe, but which
feel like they should be completely possible for people who are legends that breathe. This is Odysseus shooting through the axeheads and
And then around 15th level, the kind of stuff Herakles and Liu Bu get up to, redirecting rivers for fun and profit, staring down entire armies and mkaing them piss themselves rather than fight you, firing so may arrows it blots out the sun, that sort of thing.
It is fantastical. It is also emphatically
nothing like "magic", it isn't anything that Wizards or Clerics or Druids practice. It's physical might, personal intimidation, that sort of thing. Perhaps rolls might be required, but I would expect this to be...maybe not "lenient", but open-minded, shall we say. If it required a crit, that would be far too punitive, and getting at least
something for one's efforts (even if it comes with serious downsides) should be very achievable.
Hell, perhaps make it literal. Being a high-level fighter makes you a living legend. That's something powerful, that isn't spellcasting. Being the stuff of legends has its perks, but it also has its limits. Herakles could move a river to clean a stable. He couldn't move
at the speed of Hermes. That's still showing there are limits.
Maybe the player needs to choose one or two specific
areas they can do such Mighty Deeds in. Maybe some are charismatic and enduring, while others are strong and wily. Dunno, entirely spitballing here.
This would, of course, require extensive playtesting, because I always expect extensive playtesting for all proposed mechanics, whatever they might be doing. I would never ask of others what I don't ask of myself on this front, and I've definitely expected playtesting of others' ideas.