Maybe spoiling bc I'm at the most recent chapter so I don't remember when reveals and lore drops happen!!
I can at least answer this question for you !! She wasn't actually put in charge of the Black Tower for admin reasons -- she was put there for medical reasons! It should be mentioned by chapter 95, but Aileen has a calcified dragon heart! So mana does not flow naturally through her body, and this results in things like stunted growth rate, seizures, and apparently even a high risk of death. Her family put her in the Tower basically like life support, as well as a way to monitor her condition since the Tower seems to send in-depth reports on the tower back to the dragons.
But other than that.... yeah ur right she's canonically bad at this. She rly did only recently start reading how to do her job LMFAOOO

im on ch 95 and aileen is so fucking useless it pisses me off so bad