Maybe I formulated it wrong, she wouldn't be taken as spoils of war or reperation rather then an attmept for Aang to proof to himself that he can heal/help a single person. How else is he goona heal his entire world. Also it wroked with Zuko so why should he let her rot in some nuthouse.
Additionally, as forgivness is part of his character, he would convront her to let her know he forgives her. Of course she would laugh it off at the beginning, but she is also at her worst after the war and deprogramming Ozais work would take time.
Even outside of my personall shippdom, Ehasz himself saidn, that he planned a redemption arc for Azula with Zuko playing a central role. I just swichted out the revolving pillar.