The fighter taking out <waves> each round models which prior edition exactly as a base line?
2e. A 13+ level fighter with weapon specialization gets 5 attacks every two rounds. Figure a STR 17, and a +1 sword, and they get a +3 to hit and +4 to damage. Orcs have an AC of 6, and average hp of 4.5. The fighter will hit on a 2 or better and do at least 5 points of damage no matter what his weapon. The fighter probably has AC 0 by now, so the orcs will need a 19 or a 20 to hit him. And the same goes for skeletons, let alone the weaker foes like kobolds, goblins, gibberlings, and most humans such as bandits and guards. I think 2-3 of these type foes per round qualifies as waves.
Also, BECMI. BECMI fighters get an additional attack when they can hit their foes with a 2. So now we have a 13th level fighter, with STR 17, a +1 sword, and an Expert level of Weapon Mastery (+4), let's say with a sword. That's a +7 to-hit, which means any monster with AC of 2 or lower activates the fighter's additional attack. He rolls 2d8+3 damage: 5-19 points of damage. And if he inflicts max damage or disarms two opponents or isn't touched by an attack in a round, then he gets to force a morale check on 8 hit dice worth of creatures. Two orcs guaranteed to go down every round, and eight of them running or surrendering after getting just a taste of his prowess. Fighters also get another additional attack 24th level, and another at 36th level.
And these are still conservative examples. We're not talking fighters with 18 strength, or +3 magic weapons, or Grand Mastery of their weapon. A 24th level fighter with 18 STR, a +3 sword, and Grand Mastery gets 3 attacks when facing enemies with an AC of
-11 or worse, and does 2d6+14 points of damage (anything with 2 HD or less is killed at will). Plus he does an additional point of damage for every level of AC worse than 9 (due to Dex or magical penalties).
Even in older editions of D&D, some effort was made so that a relatively high-level fighter could mow down waves of cannon fodder.
Roland also cleaved a mountain with his sword, this models which previous edition as a base line?
None of them. Certainly not 4e. Doesn't mean that 5e shouldn't be able to model high-memetic, romantic, and mythic heroes.
Edit: And wow, this thread really moved along while I was typing that out...