DND_Reborn
The High Aldwin
First, thank you for the compliment. I know a lot of the stuff I come up with isn't for the majority of players, but I hope it helps some.Lets just clarify a few things. You have a preference for non-high level games, because you believe that tames down spellcasters to keep them from dominating play? You also refuse to accept mystic-y fighters.until past level 20?
Could you please then give some ideas for what the high (but not post-20) fighter could contribute to a party outside combat that would be as useful as the contribution that the spellcasters make? That you personally would find acceptable.
It may be that there is nothing, and we will have to accept that you just don't have anything constructive to offer the thread. But you've come up with interesting stuff before, so please take a shot.
First, building off of some of the points others have made. I think adding (again, for lack of a better term) prestige subclasses at level 12 would help. For one thing, it adds more choices to the character, which many players seem to want. Prestige features could be at 12th, 16th, and 19th, mirroring the ASI levels, so they would be uniform across all classes. Putting them at other levels could certainly work as well.
Second, your focus is on out of combat. In combat isn't as hard, so I'll focus on a couple features for exploration and social that IMO could represent high level fighters.
These examples might work for a Warlord or Fighter-Lord-type fighter. These idea could affect your allies, or "forces", or something. The wording needs work, but you'll get the idea. Certain features might be once per short or long rest, or have multiple uses, or whatever. That would need some thinking over.
Inspired March. Your presence to those around you inspires them to push themselves further than they could go alone. Any creatures within 500 feet of you that you choose have their travel pace doubled and gain advantage on Constitution saving throws to resist exhaustion when participating in a Forced March. This benefit lasts until the creatures finish a long rest.
Search and Destroy. Your ability to find your enemy is unmatched. When forces under your command make Wisdom (Perception) checks to find a hidden creature, they can use your proficiency bonus instead of their own. Targets gain no bonus to their Dexterity (Stealth) checks due to half or three-quarters cover. If you engage in combat against a discovered target, the target has disadvantage on its initiative roll.
For social, perhaps something like:
Pure Awesomeness. (Sorry, just finished watching Kung-Fu Panda

Commanding Presence. When you use give creatures orders, they tend to obey you. The creature must make a Wisdom saving throw follow your order as if affected by a Suggestion spell. The DC equals 8 + your proficiency bonus + your Charisma modifier. You can just this feature a number of times equal to your Charisma modifier and regain all spent uses when you finish a short or long rest.
So, those are just some quick thoughts. While something like Commanding Presence mimics magic, it isn't magic. The creature isn't actually charmed, which is why I wrote "as if affected by". The idea being you are so forceful in your commands that people seem compelled to obey them. Others might argue it is a fine line, but there are people IRL which seem to have this impact on others.
That's all I got for now? Thoughts?