Well if your party is nothing but human fighters, then yes. The absolute odds that someone on the party cannot climb, fly or teleport over the gap with a rope and tie it off on the other side is microscopic. Hell, a barbarian can throw a halfling as an improvised weapon up to 60 ft!
My point is that D&D doesn't consider that a meaningful challenge. Which is why you can circumvent it in so many different ways without using a spell slot. And that leads back to the problem with "nonmagical" answers. A human fighter considers this a challenge. An eladrin or aarakroca fighter does not. Is the problem with the fighter or the human now? What if your human fighter is an echo knight, eldritch knight or psi warrior? Is the problem with the fighter or with the subclasses like champion?
I ask because I feel the conversation is aimed to a specific point: it's not that the fighter cannot cross the pit, it's that he cannot do it effortlessly and NONMAGICALLY. The latter is the key. It's not that the fighter cannot get access to magical means of crossing the gap via species, subclass or feats, it's that the human champion fighter cannot do it nonmagically.
To that I say: tough.
In D&D, magic is technology. If you eschew all magic, you get left behind. I would expect the Roman legions would be mowed down by a battalion of WW2 machine gunners. Advance or die. You don't get to say the Roman legionnaires get special bulletproof shields because it's not fair, you give them freaking firearms. If the fighter is left behind because it's non magical then make. him. magical.
The issue isn't with the fighter. The issue is with nonmagical. The fix is easy after that.