If you check which units have the "scare" trait, you will find the elephants, chariots, drugged naked swordmen, naked spearmen and the mercenary half naked axemen. They are special units, not regular ones.

Now if you give this trait to the pikemen, then the well armored heavy cavalry and archers such as Cretans should get it too, because they were as much fearful as the phalanxes. Also the Imperial legionaries would have it too, because by the time the Augustan reforms happen, Rome is a superpower with her feared legions. And the whole game would need a rebalance too.

So I think it's a bad idea.