Aragorn is worth more than a thousand mail-clad knights but much of it is because of all sorts of reasons utterly external to the things a fighter or even a wizard in D&D have and do. Aragorn is significant in the eyes of Sauron because, fundamentally, he has the right to counter Sauron's might. That's how he wrests control of the palantir - because it is his by right. Why is he a significant leader of men? Because it is his birthright, his destiny. These concepts are pretty big thematic elements of Lord of the Rings. And none of that are really things D&D has done much modeling of outside of Birthright because they are (and should be) highly campaign dependent.
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.I want high-level PCs to be powerful - legendary even - but even legendary heroes have to be vulnerable to some threat (and not just an exceptional one that has to be contrivedly summoned every adventure), and it has to have some relation to reality.
I'd rather that the majority of their power comes from their political influence or (by that stage) leadership of fiefdoms/kingdoms, not from how they can single-handedly defeat any army on the planet*.
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.
High level magic-users, though, are one-man reaping machines on the battlefield. Does over 100 hp of damage to 4 areas of 40' R - which is to say that it effectively wipes out dozens of knights in mere seconds. Or destroys whole encampments or villages.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
<snip>
This is the sort of thing that is up to the DM and the players.
<snip>
To me, it just seems stupid to have 20th-level characters being one-man reaping machines on the battlefield
I don't understand why we need rules or mechanics for everything.
Which is why nobody is asking for that. What people are asking for are rules and guidelines for building domains and influence. Which aren't exactly fringe cases it's safe to make up as you go along.
We might. But I'm rather exasperated that whenever someone points out that something could or should be covered by the rules, the response is invariably a dismissive statement that "we don't need rules for everything, figure it out yourself". A rule you can ignore or alter is generally better than not having rules for something, within reason and word count.
As far as fighters fighting off armies go, I treat it as a purely academic question - the fight is going to be a wonderful cure for insomnia either way, so why bother? I think some mass combat rules are planned - maybe they'll make it actually worth playing out.
You're playing the wrong game, pick up a superhero game. Level 20 martial characters in D&D do not have fantastical abilities simply by the fact that they're 20, and definitely not by the fact that, as you imply, they have more HP. More HP just means better ability to not suffer a killing blow.
Not to mention: in the real, mundane, world, it is possible to kill or disable someone with a single sword-stroke. There is no reason, as far as realism is concerned, for spell casters to be the only D&D characters able to circumvent the hit point system in combat.
The balance for wizads then lies in their utility, non-combat abilities.
That is a great steaming pile of freshly laid self-righteous victemhood. And it's completly false on many, many levels.
First D&D is much more closely tied to literary heros and tropes than to mythic ones. There are games tied to Myth, D&D is not and never has been one of them.
Furthermore those literary influences contain large chunks of the Swords and Sorcery genre where magic is not easy, and never free.
Secondly while you are proudly claiming victemhood your are rather pointedly ignoring the simple fact that a Class designed to play as Hercules cannot also portray Fafhred and Conan. Why is it you must be allowed your perferred playstyle, but others cannot?
Thirdly, this means your claim that the conflict is miscast is patently false. Worse you're disingenuous even about your own goals. A "Mythic Hero" class won't cut it, it must be a fighter, even a Totem barbarian is too far for you to bend. Why?
Fourth the heroes you cite are not mortal, mundane characters, except possibly Beowulf whose ancestry and training are not gone into as best I recall. Hercules is a demigod. Chu Chulain was trained and armed by supernatural powers.
To be clear though, a level 20 fighter in 5e can kill almost anything in the world in under 20 seconds. So Samwise Gamgee he ain't.

(Dungeons & Dragons)
Rulebook featuring "high magic" options, including a host of new spells.