The Elephants not only have weak moral, they have both high hit points and low defense/protection. So they'll take and soak up a lot of hits, which is good, but each of these hits will force a moral check on them, which is bad. So Elephant will rout after what looks like only light losses, unless you factor in all those hits they took that didn't kill them...
My own favorite strategy with them is to put a heavy infantry squad front and slightly to the side, and the elephant at the same side, back a bit, on hold and attack. The fact the heavy infantry is offset means that the enemy will tend to end up on the open (center) side, with only a few on the other side. Then the elephants come in, and they demolish the weak flank of the enemy, which is already well engaged by my infantry, meaning the elephants don't take many hits and don't get mobbed. Well executed, this means the elephants don't take losses, and the enemy routs with elephants on its tail (guess what happens to them
). The only catch is that the heavy infantry must be able to hold its own for 3 or so turns, while being outflanked on the open side...