Barbarian magic suppression skills...

Would you really ignore your subordinate Warlords?!?! They wouldn't ignore you either! So you're wrong about Anti-Summon. And as for the Executioners, they would have reached you and at least hit you a couple of times. In the end, getting beaten by your own troops is unpleasant in any case - not just by Executioners, but also by a Cyclops (berserker). I mentioned the Executioners because your Phoenix would have a hard time. And as for the statement that "with Anti-Summon, he could have won" - that's complete nonsense; you would have simply crushed him with Darkness (which includes much more than just Subjugation).

The Phoenix played the main role. It took out the Orcs like it was nothing. And Anti-Summon would significantly reduce its effectiveness. And the Shield wouldn't be as strong. You would have to summon a new one... Okay, to avoid being unsubstantiated, I'll post a replay of an experimental 500 Challenge Dungeon run - take a look at what "creatures" Lethos and Necromancers can have in combination with Darkness + Summon, and I think you'll understand that it's better to have Subjugation last longer, even if it means a weaker bird...

P.S. Only Vampirism is used from Darkness. And it can't be reduced much, which means the Phoenix is immortal...