Unjust deaths of mindless automatons which could kill many mortals but have a finite time of activity? Come on!
That's among the most easily explained and logical things - if they don't have weakness in morale, they should have something else instead of it! Actually, I know a tabletop wargame which uses similar mechanism and it's quite popular.
And if Golems wouldn't have this weakness, they should be much more costly.
