"Hawkman regrets the death of so many birds... but this is war, they are his army"
No, they are sodding well not, you malevolent, bird-murdering bastard Hawkman!
They are non-sentient animals with no vested interest in what you are forcing them to do. If anything they are, metaphorically, civilian non-combatants you have forcibly drafted into your feathery Suicide Squad!
Now if we were to find out that these are grateful birds who are doing it in return for your protecting their endangered habitat, then it's not quite so bad, but we haven't seen any indication of that.