I think it could lead to some interesting situations.
Like what if you're sneaking around the castle of a known enemy. You encounter a bunch of guards, you see no alternative and you fight. Their morale breaks as the battle progresses and the last survivor(s) tries to flee, hoping to find reinforcements. Do you risk him going after him to stop him from alerting the castle, even though that may mean exposing your party to surprise attacks or other encounters, or do you allow him to go free to alert the rest of the castle and bunker down? Or do you use the opportunity to escape and try again another time?
Or, to take Jarmo's idea a bit further, you could have certain enemies attempt to surrender to you. The majority of enemies would either flee or fight to the death, but certain NPCs could yield to the party leading to some interesting interactions/options.
You could also implement the mechanic into formations, where certain formations give a boost to morale and having a formation break because you're getting overrun/flanked intensifies the rate of morale loss.