Hit points clearly don't simulate *anything* really, except how close a character is to death.
In 4e, not even necessarily death, just defeat - when you drop someone to 0, you can decide what happens to them, just KO them or whatever, instead of leaving them dying.
Whether meat or morale, being low on hit points doesn't affect your performance (barring a few exceptions like bloodied dragonborn and the like) whatsoever nor does it have any direct bearing on your character's fictional positioning.
In 4e, Bloodied can bear on both. And, you already have separate-from-hd conditions (and can arbitrarily apply just about anything in the same manner, thanks to exception-based design), breaking an enemy's morale (temporarily if the fight isn't all but over) could be rattled, dazed or even stunned, for instance.
My experience with the Intimidate skill's morale effect is it almost never gets used. The DC is high enough that, unless a character is super-optimized for a high Intimidate bonus, it is absolutely not worth the effort to waste a standard action on it during a combat situation.
Matches my experience.
One minor variation, apart from just having enemies break and run or break & surrender when it seems reasonable, would be to set lower DCs for it when the tide has clearly turned against their side and/or they're prone to surrender or run for any other reason...
I disagree with AbdulAlhazred's assertion that having a "second path" to defeating enemies is problematic, especially in a Story Now style of game. In fact, opening thematically appropriate avenues toward resolving encounters is pretty much intrinsic to Story Now type games. I actually go further than this in my own games, and often have Skill Challenges operating in tandem with Combat Encounters with the PCs able to "win" the encounter using either approach. The morale system I described is just icing on the cake.
Using a Skill Challenge structure parallel to the combat I could see, yes. It gives you a separate path to resolution.
The advantage of Abdul's approach is that it keeps the system 'simple' (less complicated? more elegant?), by using the existing mechanisms - hps, healing/regen, damage/conditions, traits, to model enemies with unusually good or poor morale. It seems like more than a few powers also want to model shaking enemy morale in various ways, already, too.
The skill challenge solution would share that advantage.