So, the question is, why doesn't Aura work as aggressively as it should? Warriors move quickly with empathy(((

It's not the warriors who move quickly, but the hero with empathy.

The bonus for Haven at level 20 is +1 Initiative. That is, instead of 10, like everyone else, it's 11. Not that much.

Often, for the late game, light magic is useful for Academy, but you can also try dark magic (it depends on the opponent).

For mass spells, enchantment is generally useless, especially in the late game when there will also be a huge amount of mana (unless you take counterspell).

And in the late game, without minions, the Academy hero is doomed.
Defense is essential.

The enemy will most likely cast Slow or Haste, if they can, so you need to be prepared.