So we have two different groups of people:
1: One group does not care that martials don't get anything cool, because if they got something cool it would make their play experience worse
TBF, it sounds like they care. Not caring would mean they feel whether martials get anything 'cool' or not has no bearing on their play experience. That'd be a third group. Does this group not exist? or is it perhaps some excluded middle? Or just not relevant?
2: Another group feels like the fact that martials don't get anything cool makes their gameplay experience worse, because there is nothing to look forward to as you level up.
I think there's an issue with the definition of 'martial' excluding spells, because, like, an EK or a Paladin surely, as a skilled weapon-wielder with the same chance to hit as a fighter and the Extra Attack feature, has 'martial skills' while having 4th or even 5th level spells as cool stuff to look forward to. Or, like, an Echo Knight is a fighter with the same Action-Surging, Extra-Attacking glory as other fighters, and some cool supernatural stuff from low level on.

The issue being spells (or on occasion some other supernatural power - but considering the ultimate handling of 5e psionics, basically just spells going forward) are just
the 5e mechanic for being able to do anything high-level-'cool.'
I believe that for this reason the only reasonable solution to the balance problem is to have an entirely separate martial class that is essentially an "unchained" fighter, one that is properly balanced against the the stronger classes.
I could see something like this working fairly easily in 5e.2024, if there were any impetus at all to fix the issue - which, lets face it, 5e restored and then enjoyed tremendous commercial success, so from the exec pov, there is every reason to preserve the issue indefinitely, if not lean into it somehow - since MCing is expected to become core. You could simply have some classes with no higher levels, at all. Fighter could stop at 9th, for instance, or 6th, or exist only in Tier 1 - wherever you set the bar for mundanity no longer being competitive. From there, the player would have to choose some other class - or Prestige Class. So an "unchained" fighter with nominally non-supernatural but functionally balanced abilities could be an optional PrC that DMs can allow if they want that sort of thing in their campaign, otherwise, things like Eldritch Knight or Echo Knight or Rune Knight or whatever, could open up as PrCs instead of being sub-classes.
But, while it could work, even the idea of all classes having sub-classes kick in at the same level has been rejected, so, like all other reasonable, even possible, solutions, not a
realistic practicable option.