It just comes down to balance issues, like this very thread. People see the disparity between martials and casters, because they aren't blind.
It does depend on what you are comparing though. If you look at combat damage the fighter comes out well most of the time. However, for shear utility the magic users are far and away superior (as long as they don't run out of slots of course).
There are two solutions. Try to nerf casters, which the system really isn't mean to do (there are issues inherent to the system that casters are apparently designed to solve- there's a sidebar in Xanathar's that discusses this point when it comes to resistance to non-magical b/p/s damage), or to do work on the back end to make sure your caster light/no caster party doesn't encounter these, or have other ways to deal with them.
I have suggested a few "nerfs" in this thread that I think overcome most of these issues. Then again, I haven't done a deep dive and this are a bit off the cuff.
Or to take the limiters off the martials and allow them to have "supernatural" abilities of their own. There is a bias on the part of the game designers- they look at a subclass and say "ok well, they are magic, so they can have any kind of cool ability", then look at another and say "oh this guy can't have magic. better give him...uh, I don't know, advantage on an ability check or something".
It is not just designers, as this thread shows. Some people are adamant that their martials can only do mundane things. I think that is a completely legitimate way to play. The difficult is making one ruleset to accommodate both ideas.
I understand the desire to have a narrative of the "ordinary man in an extraordinary situation" but even 4e ran into problems here. Any power source other than Martial could, for example, get a power to teleport. And the Ranger actually got such a power because they had a slice of the Primal power source.
So there was this entire design space that the majority of the other classes could have, that was locked off from the Martial classes because "that's too magical". By contrast, there was nothing unique to Martials that other power sources couldn't have.
Sure, but not everyone sees it that way. Heck, you could easily make a version of the Eldritch Knight that could take misty step to gain a teleport. You could even re-fluff as a martial action if you want (lots of martial-arts theme fiction has abilities like this)
But there will always be a segment that will only accept these as magical abilities and that is OK.
I think there is a way to achieve both with the same ruleset, but you probably have to accept that your really playing to different games that happen to share the same (or at least some of the same) rules.
So for the health of the game, the narrative should change, because otherwise, in order to have the desired narrative, you have to spend a lot of time and energy undoing what the developers have done to the game.
I don't really think it takes that much to change it, depending on what your goal is. The issue is that different people have different goals. I mean I can fairly easily make 5e a low or no magic game. I can even keep all of a casters spells and spell levels while doing it and making it a bit more balanced with martials. With a little more work I can give fighters most of, if not all, of the versatility of wizards.
Ideally, 5e would provide different module to do these things, which it could, rather than leave it up to us DMs. Then again, I sure I would prefer what I come up with versus what WotC would come up with.