But the question becomes, how can you present that horde of enemies without one of the following being true:
1) The enemies are designed to be a valid threat to the PCs, but individually easy to defeat (such as 4E minions).
2) The enemies are designed as a large number of lower-level enemies, not necessarily dying in one hit, but also not presenting a genuine threat.
3) The enemies are designed as genuine threats to the PCs, providing a real feeling of success if they triumph - but more likely leading to the PCs being overwhelmed and defeated.
Keep in mind, a minion being individually easy to take out doesn't mean an
encounter with them will be just as easy. Hacking down a single enemy might not provide that feeling of accomplishment you are after - but wading through a sea of enemies and emerging triumphant? I've seen players accomplish that, and be genuinely excited at doing so.
Mechanics aside for a moment, it isn't the feat of rolling a particular set of numbers on some die rolls that is satisfying. The satisfaction is in knowing that when an opponent drops (or doesn't) that it is a creature that feels like it belongs with the rest of the world.
So what is your solution? Never have a fight in which the PCs face a horde of enemies? Since your only options are lower-level enemies that can't threaten the group - or threatening enemies that are thus overwhelming. Which might be acceptable for very occasional combats, if the PCs prove lucky enough to survive or escape - but would by and large remove that entire category of encounters from being an option.
And that aside - when a player drops a minion, that creatures feels like it belongs with the rest of the world. When my soldier cleaves through a half-dozen orcs on the way to the orc chieftain, it feels appropriate they died easily - they are regular orcs, unable to stand up to the blows of a mighty warrior. What is out of place about that?
I mean - tying this to classic fantasy stories, how often do we see an author describe the hero having to swing a half-dozen times to drop
every single enemy in his path? We don't - the hero cuts down lesser enemies with ease. Quite often with single blows! At the same time, he doesn't dismiss them - if he leaves himself open, even the least opponent could land a serious blow.
And in some ways, enemies dying in one hit and everything being a threat could be argued to be even more realistic than the alternatives. Honestly, it is the PCs themselves, and the stronger enemies they face who take dozens of attacks to drop, that aren't 'realistic'. Which most people accept, because its a game, and having every character die as soon as they take a single hit from a sword just isn't all that fun.