The part about personalities that - stick - makes sense. She thinks not having free will helps with that? But in case it doesn't help enough she tries to pull together why the parts of Asmodia - come from underlying traits, instead of just being all of the most useful traits for a person to have.
Maybe Asmodia - derives satisfaction from intellectual things, not physical ones; her state and the state of the world are interesting information, and useful, they're how she'll shape the world, but they're not intrinsically motivating the way that service to Asmodeus and better understanding of Asmodeus and progress towards a perfected world are interesting. That's why she doesn't care about food or sex except instrumentally; the things that speak to her soul are bigger. But - there's an obvious failure mode here, she's met people who fell into it, caught in an endless cycle of apparent insight and epiphany, never really accomplishing anything, so -
She chews over it for a while. She wishes she could talk to an actual priest. Carissa is mostly devoted to Asmodeus because otherwise she will get crushed like a bug - or, apparently, dissolve and cease existing - and this is not a threatening state of affairs. Asmodeus knows that humans are weak and pathetic. Asmodeus will use the bits he can no matter how contemptible he considers her motives - but it doesn't seem quite right for being a priest of his.
Maybe Asmodia feels, sometimes, when she's accomplished something really meaningful for her cause, a glimpse of what a valuable life is like, what Asmodeus cares about, and she's driven by that, by wanting to serve it and hoping to feel a bit more of it. Is that the right kind of underlying personality? It feels - closer. It's not a grab-bag of traits.
She reads the books and tries to make money faster than she spends it so she can save up for clothes.