Why is that bad? Isn't there room in the game for a couple of classes that do single target damage and combat better than everyone else? Does everyone need to be active in other pillars?
The problem is the fighter isn't better than single target damage than everyone else. And he definitely isn't better at "combat". But he is dead last when it comes to usefulness outside of combat. That is fine, I guess. But the rogue can be just as good at single target damage, while also providing tons of non combat utility so clearly being good at combat doesn't have to come at the expense of non combat capability.
I've found that too many characters participating in every pillar slows the game down. You don't want everyone trying to be the face. You don't want everyone scouting. You don't want everyone making a knowledge check. What's wrong with having a guy in the group who shines brightest in battle?
With a name like fighter, they probably should shine brightest in battle. But that doesn't mean they shouldn't also be moderately capable outside of combat. I'm not saying they should be great everything. I'm not saying they should even be great at many things. But they are literally the worst class outside of combat. And not by a small margin either.
Can you provide some examples of what you're wanting for out of combat abilities? As well as reasons why you can't multiclass to create the archetype? Why does it need to be something you should be able to do playing a single class fighter?
Honestly it doesn't need to be the fighter. I think we would need to rebuild the class from the ground up to make it worthwhile or interesting. I'm completely fine with the legacy of the fighter being in 5e exactly what it was in 3e and 2e; A boring, repetitive, and simple class for newb players or grognarda who don't want to bother with tactical decisions or complexity. I'm fine with the fighter being the worst class when it comes to accomplishing tasks outside of combat. I merely want a martial warrior who is more representative of "fighters" from myth, legend, and fantasy.
Here are some possible ideas for non combat abilities for a mythic martial warrior (maybe in the form of special talents which are like warlock invocations but for martial warriors).
Larger than Life
You have proficiency with STR checks and your carrying capacity is doubled. You can also grapple or shove creatures as if you were one size larger.
Endurance
You have proficiency in Con checks and you recover 1 level of exhaustion whenever you complete a short rest.
Strength of Legends
You gain expertise is Athletics checks and your carrying capacity is doubled (yes, 2 doubles quadruples your carrying capacity).
Mighty Leap
Double the distance of any jump you make.
Leap of the Clouds
Your high jump distance is equal to your long jump distance.
Peerless Athletics
You gain a climb speed and a swim speed equal to your speed.
Demolisher
You have advantage on STR checks to break objects and your melee attacks deal double damage to objects and structures.
Mark of Prestige
You gain a mark of prestige (as detailed in the DMG).
Hero's Charm
You have advantage on Charisma (Persuasion) checks. When you successfully persuade a non-hostile creature, that creature is Charmed by you for 1 hour. While charmed, it treats you as a friend. The effect ends if you or one of your allies act in a hostile manner towards your new "friend".
Villain's Menace
You have advantage on Charisma (Intimidation) checks. When you successfully intimidate a creature, that creature is frightened by you for 1 minute. The frightened creature can make a Wisdom saving throw (DC = 8 + your proficiency bonus + your Charisma modifier) at the end of each of its turns to end this effect.