Not killing Alicia is very inline with Aura's character, and it doesn't have anything to do with being prude or morally good or anything like that.
Spoilers below.
She's arrogant and prideful, time and time again it's been shown through the game.
There's a reason why getting the Curse of Pride didn't do a single thing on her, she's already full of it.
Go back to the first conversation when Alicia infiltrates her mind and meets with the Guide Aura. The Guide Aura literally says she will help her corrupt herself, because she already expects to fail. Because she's too proud to ever believe Alicia could overpower her willpower.
And yes, you might find that stupid or annoying, but it's definitely not out of character.
Especially cause the game showed so many times how Aura isn't that different in her character from the Demon Generals. Except she's on the side of good instead of evil.
I for one really like this character flaw of hers. Makes her more memorable than just some pure good girl who gets corrupted just because she was unlucky or "punished for doing good". She was too proud and either gets punished for it, or not, depending on your choices.