They could make the simple fighter feel better in a few easy ways by adding onto their 11th level+ features with things like:
- A guaranteed called shot feature that lets a fighter inflict conditions for hitting consecutive attacks on the same round.
- The ability to deal 10x their level in damage when they hit a successful attack once per long rest for huge spike damage, representing how lethal the fighter is with a weapon in hand.
- The ability to treat any improvised object as another weapon of their choice, catching the movie fluff of the fighter just picking up random stuff and kicking butt with it.
- The ability to strike an opponent so hard you lower their maximum hit points.
- The ability to figure out how an enemy fights and neutralize any modifiers to its attacks.
- The ability to combo attack with an ally's reaction against a target in range.
- The ability to predict a creature's turn in battle and interrupt it, dealing critical damage and ending their turn immediately.
- The ability to reroll initiative for other creatures in combat through orders or intimidation.
- The ability to apply any weapon mastery of their choice to any weapon, showcasing their ungodly skill with armaments.
- The ability to immediately attune to a magic weapon, armor, or shield through raw experience.
- The ability to use the environment to deal other kinds of damage with a weapon attack.
Just a handful of these features, each of which is incredibly simple, could give the Fighter a little bit of juice while keeping it streamlined for casual play. Since high-level play also involves way more involvement from the players, you could even make it a grabbag and every fighter picks their favorite "Epic Triumphs of Skill" at odd-numbered levels from 11th onward.
Simple solutions like these could give the fighter greater appeal to players who like a little more juice to their gameplay. You could even say at each odd-numbered level, you receive X thing OR you can choose from the options below. This means that you can just take the typical level up or get a little custom with it.
All of these features would be easy to flavor as either grounded or mythic. You can immediately attune to that magic sword because you know every sword as well as you do your own body. OR you can do so because you're the stuff of legend and magic weapons want to be in your story. Etc etc.
I know we won't get this kind of stuff from WotC at this point, but I'm really sharing these ideas as a proof of concept that yes, you can have a slightly more exciting fighter without compromising at ALL on complexity.