Ap or Altap

Here I see an effect, not just some numbers like -1 to morale.

Actually, it's -3 morale, which is quite a lot. Without the fear attack, the horses are useless because they'll die from the first counterattack.

Support for the archers and the hero is definitely needed, and there are still quite a few melee units.

The problem is that these melee units die very quickly (meaning the dogs and horses). In late-game battles, you need a larger unit with a powerful attack, which is what the offsprings provide.