In fact AD&D modelled a fighter's right to rule fairly clearly - at 9th level s/he got an army that a wizard didn't. There are pros and cons to this as a mechanical approach to the issue, but it was there as part of the game.
Where are the mechanics to support a fighter's leadership? Eg bonuses to CHA? Automatic relationships with key NPCs? Men-at-arms in the style of classic D&D? Etc. If this is where a high level fighter's powers is expected to come from, where is the rules support? Reading the Basic 5e PDF, a wizard is as likely to have these sorts of resources as a fighter, perhaps even moreso because s/he can probably better afford to pump CHA as a secondary stat after INT.
I don't understand why we need
rules or
mechanics for everything. If a character makes it to, say, 10th-level (or whatever feels right for the campaign), then it's likely that he/she will have accumulated allies and influence. Maybe not - it depends on the campaign and the setting. In my setting, which is a Feudal one, it's probably time for the characters to gain control of (or set up) Baronies, if they so wish.
It doesn't matter to me whether the character is a Fighter or a Wizard. It will be their reputation, contacts and wealth which will determine whether they can do this, not their personal prowess in battle (this is not a tribal society where personal fighting prowess decides who gets to rule; although "might makes right" probably prevails, "might" could mean skill with magic or diplomacy).
This is the sort of thing that is up to the DM and the players. I think there are going to be rules for how to run dominions in the DMG, but that's beside the point - gaining more political influence will emerge naturally in many settings (and not at all in others). It will either fit the setting, story and players' tastes, or it won't.
Bringing it back to the topic in hand, by high level characters will be formidable opponents in one-on-one combat, but in my view, their power should really lie in things other than fighting prowess. To me, it just seems stupid to have 20th-level characters being one-man reaping machines on the battlefield. Sure, they might turn the tide of a battle, but not by single-handedly killing the entire enemy army. For me, it's much more convincing - and appealing - that by this stage their interests lie in influencing the world around them through political power, rather than personally thinning the enemy ranks (although they might still do plenty of quests between the politicking).
Of course, if other groups want to have one-man death machines, they could handle this by dishing out lots of magic items, or giving characters lots of feats, bumping their hit points, allowing progression beyond 20th level (by home-brewing extra levels), etc. It's much, much easier to do a monty haul campaign in any system than a restrained one; therefore I say the rules should produce more down-to-earth characters; DMs can easily throw in the "epic" if they wish.