As others have pointed out, high level characters aren't air power, they're everything power. However, looking at this a bit closer, a few things will become apparent:
1. Magic and magic items have dramatically different effects in a mass combat situation than in a skirmish situation. Normal D&D is a skirmish situation. Barbarian DR, Armor of invulnerability or admantine armor is nice but not a really big deal because you're taking a few hits for several dozen points of damage per hit--often from a magic weapon. In a mass combat situation, however, you may have 200 archers firing at you, each of whom hits only on a 20. So that's 20 hits for 4.5 points of damage each. Stoneskin or Protection from arrows? Nearly gone in 6 seconds. Armor of invulnerability? You take approximately 10 points of damage instead of 90. Adamantine armor, barbarian DR, or Righteous Might will have a similar effect.
Similarly, in a normal D&D skirmishes, flame strike and fireball compete as good sources of mass damage. In a mass battle, however, they are far less useful. Sure, fireball may well incinerate 40 foes in a very tight formation, but your unit of 200 archers can do at least as well. (And which is easier and cheaper to field? 200 archers or an arcanist powerful enough to launch 20 fireballs? (Assuming your archers carry 20 arrows) And which is harder for your enemies to kill?)
Fireball is not the big deal a lot of people think it is. Now, enter spells like firestorm, sunburst, and holy word. In the skirmish, they have their uses, but their full potential becomes apparent when you can fill up their entire areas with enemies. Those spells will devastate large armies. Fireball won't.
Third, range becomes a much more serious factor in large battlefield encounters. In the skirmish game, fireball and flamestrike are comparable. In a large, set battle, the ability to target foes six hundred feet away (only the 4th range increment for ordinary longbows) instead of having to wait until they're 200 feet way is a massive advantage for fireball. In practice, the importance of range means that feats like Enlarge Spell become much more significant. It also means that a lot of spells that seem like they would be useful--wall of force, lightning bolt, cone of cold, etc, are severly handicapped.
Even mundane equipment changes its usefulness. Tower Shields are OK in normal D&D. They offer always on Combat Expertise for fighters without Int. In a mass combat situation, however, the take cover option provides characters with immunity to archers. Tower shields are what give melee troops the ability to advance across an open field under fire from archers. Otherwise, they just get slaughtered. (So, to review, for PCs, tower shields=OK; for armies, tower shields=necessity).
2. Feats also make some very significant changes. Great Cleave and Combat Reflexes are particularly notable in this regard. Great Cleave is the reason that the high level blackguard duels the paladin one on one instead of mobbing him with his minions. The paladin would just great cleave through the minions and would therefore hit the blackguard just as often as if he had no minions there at all. Combat Reflexes and reach turn those minions into a positive liability if the character has great cleave. Each time a minion provokes an AoO, the blackguard loses a minion, and gets hit on the cleave.
3. As has been explored in other places, high level characters can do a lot. The one thing, however, that they cannot do is be everywhere at once. In Greyhawk, for instance, a high level barbarian might be able to hold the gates of Crockport against Iuz's footsoldiers for hours, but he won't be able to do that and hold the south wall where Iuz's minions have climbed up and are setting fire to the city.
4. The discussion of "high level" characters and mooks misses the very important in between ground of mid-level characters. The evil blackguard/barbarian can be wearing a fur loincloth and still doesn't need to fear mooks. A score of mid level paladins with spirited charge, however, will smite him into the ground in less than a round. Similarly, while a high level mage can devastate armies with sunburst, a group of mid-level mages with scorching ray or reciprocal gyre can ruin his day just as quickly as he slaughters the mooks. Mid level characters don't have the ability to reliably destroy large armies by themselves. However, they can be integral parts of those large armies and they are a significant threat to high-level characters.