This page on CWB rules for multiplayer in Rome Total War says that elephants are not permitted in multiplayer not because they are OP, but because they are easy to counter.
That doesn't sound right to me. Sure, if you try to rush the elephants up front, most probably they will be showered by flaming arrows and they will run amok but if you keep them out of the missile range until the last minute (which the infantry engages), then you will safely rush the elephants to the flanks of the enemy and sink their morale and make them rout and hence, win the battle.
So I think the real cause elephants are prevented is because they are overpowered. What do you think the real cause is?