Thinking it through again...Do you think any of the patron librarians can go with us too if you are working on that logic?
Or the assistants? Or the magical girls?
Are we really depending on the Head not being anal about a ruling as a reason here?
The patron librarians, librarians and magical girls all are stuck in the library by the fact their bodies are made of light and can't get out.
We were explicitly told we could go to the city ourself, and there is no rule lawyering involved, we are associated with the library but not known as such, and we are not identifiable as a patron librarian as easily due to being an abnormality.
Lepi said we could search answers in the city, I see no reason to think it was a trap option at the time, nor any reasons to think this fact changed since then.
It's not so much that X thinks Kyoko is stronger than her as she thinks the girl needs a confidence boost right about now.
She didn't say it out loud though, just thought it, and X does have an impostor syndrome, that much is true.
Edit:
To expand on the *Not a trap option* thing I said:
When we got the vote, we rejected it on the basis of not wanting anything to do with the wings and not wanting to get into the city's drama, which is a logical conclusion to infer from the fact that the options were given in the first place, what would be a trap option would have been us deciding to go see the wings or searching in the city only to get a *ha ha! You get ganked by arbiters as soon as you enter the city, they kill you because you're a librarian and entered*, which is not a reasonable thing to infer due to the fact that the option to enter the city was given to us in the first place.
The easy way to explain that is simply to see that the Head specifically banished the library from the city, meaning that Angela definitely cannot return, but the librarians probably could if she finds a way to set them free of the library (except for Binah, she would probably get ganked), meaning that as a patron librarian able to leave the library, we can enter without any problems.