I think it helps her seem more realistic. Especially when it comes to her decision making as she does like him, but is really changing and finding happiness for him. Rather than for him to go down that painful and dark path of the novel. It's relatable to hesitate at moments that concern a whole lot of thinking as every movement she makes and what she speaks changes the whole novels story. (Plus, she ended up being the novels mc females twin sister that didn't have one at first.) Most stories she would've been the lead girl instead (besides her actually being the mc of this webtoon) and a love triangle. I'm glad she wasn't. So that she could have the chance to try to be with him. Just my thoughts.
The reason she is hesitated because she doesn't even know why she comes here, ok?!?
Just think about it yourself, what if you suddenly be transfer to the manga you like and you know your fav char will die!!!
Of course you wanna save him/her without changing too much the story, so that's why she likes that, ok?
And if you still not like her personality, then why don't just quiet and watch or leave?
You have to understand the author create her like that to attract Aseph so just accept, ok?