I have found that teachers' awareness of the breadth of literature is stagnant. When students need books for book reports or other projects, the teachers give suggestions that were outdated, limited, and not always at the right level to comfortably challenge the students. I am much more skilled at connecting kids with the right books for their needs and interests. In addition, my knowledge of the collection means that I can locate specific materials many times faster than people who only visit occasionally.
Information literacy and digital citizenship are important areas of knowledge today, and a librarian is trained and placed to teach these lessons or coordinate with classroom teachers. In spite of the ubiquitous assumption that "everything is on the internet now", most laypeople do not know how to precisely locate information or judge the differences in quality and validity among different sources. Students need to specific education in how to do this, and librarians are the people for that job. They can provide valuable co-curricular classes in research and information literacy, which takes the pressure off teachers to create and include lessons in these matters. School libraries should provide access to subscription online information databases: Google alone is usually not enough.
Limiting students to classroom libraries for "fun" materials means that many kids will never come across books that they will love. Variations in interests and reading levels can be vast within a single class, and many students will not bother to pick up books without external encouragement. Those who read either above or below "grade level" will not have access to books that they can and should enjoy.
Having a beit midrash is wonderful, but who maintains order there, so that students can find what they seek? Who updates the collection with new materials and replaces old/outdated ones? A librarian's professional input is as valuable there as in the library proper.
