I hardly played 2E so I'm not sure how morale was handled in that version, I'm going off of AD&D.
Flipping through to page 67 of the DMG it was made quite clear that morale was only used for "non-leader NPCs" and "intelligent opponent monsters", just to clear up any confusion people might have that morale was intended for PCs.
Looking over the rules it looked like the DM I had that used it often must have had a much simpler system, because I know he didn't use all of the percentages and modifiers that the official rules used. My foggy memory recalls something more like:
If the leader is slain and there are more PCs standing than monsters then 50% each turn the rest will run.
I know he was just rolling a d6 to see if they fled.
In the games we played the morale only seemed to be used for intelligent humanoid types, like orcs, town guards, goblins, etc.
One of the big perks of morale was that if you did break the enemy and made them flee (and to point out, the morale roll was for the whole group of monsters) was that you'd get a free attack with huge bonuses to hit as they fled, using the rules pg. 70 of the DMG. So when those goblins freaked out and ran it usually meant all of them getting hit and mowed down as they turn and fled.
What also allowed morale to give a lot of flavor was that while some monsters did have morale, others did not. Skeletons and zombies were more creepy because you couldn't break them, they just kept marching forward and you had to smash and slash them all to pieces.
I do think it is unfortunate that they discarded morale. I think with all of the other math that got pumped into 3E that they could have come up with a streamlined system with strait forward conditions, and also be able to factor the creature's "break" value into their final CR value.
While DMs can and do toss off the cuff morale into their games, the fact that the rules don't highlight standard psychology creates the overall effect that there isn't any, and so it's only been in 3E that I've seen the standard situation is that creatures fight to the death. The only times I've seen DMs use morale was usually when they wanted to bring a scene to a close, knowing that it was only a mop up situation at that point. It never seemed to be weighed as a real strategy to try and break the enemy, which is unfortunate as that is a big factor in real conflicts.
The funny thing I've noticed is that what is left of morale in 3E is mainly only applying to PCs and not to monsters. For the most part the fear effects are things monsters perform on PCs. The end result is that most fear effects involve a player running from an encounter and the player have tons of fun waiting for several minutes to pass in-game before they can get back in the action. Thus they have to sit around, or go grab something to eat, or play on the xbox, while everyone else plays.
True, you can demoralize with intimidate, and spellcasters can cast some spells, but... come on... how often are spellcasters casting those spells, and you can't (surprise!) see the fighter driving his enemies before him.
Another effect is that in living games like Living Greyhawk and Pathfinder Society, because you need to stick to RAW as much as possible, it also disinclines DMs to use off the cuff morale house rules and thus even more games go without guidelines that would help breath a bit more realism into the fights.
I certainly wouldn't have wanted to see the rules in the AD&D DMG retained after all of these years, but a revised system would have been great, offering a viable mundane strategy to the game and making things feel less like a video game where the icon of the monster just keeps swinging until its health bar is gone.