How does librarian teaching expertise benefit students and teachers?

Because librarians have classroom experience, they understand what current classroom teachers need as they build lesson plans. As they work with teachers, they bring into play their additional training in books for all levels, in finding new useful books and digital resources, and in offering creative approaches to expand classroom learning. The school gets effectively two teachers for each classroom, though one is working from the library and working with all the teachers all year long.
 
When there is no library, teachers lose not only the person but effective access to whatever collection may remain on the campus. And students lose more – the librarians is able to help them select “just-right-for-me” books each time they visit. Teachers can’t know what books are in the library that might help them – that might suit a specific struggling student, that might help teach that concept kids are struggling with, or that will be the perfect read-aloud to lift enthusiasm for reading generally. All of these losses directly impact student literacy and student test scores. When the library remains but staffed by a person without library certification, teachers get only some of the skills they should be relying on.​

Here's an article with more information:
​Gaffney, Loretta. "School Librarians’ Knowledge: What We Bring to the Curricular Table." KQ, AASL, 11 Jan. 2018.

https://confessionsofateacherlibrarian.wordpress.com/2013/03/29/the-priorities-of-a-teacher-librarian/