The habit of reading needs to be inculcated from childhood itself. While we were kids we happened to hear bedtime stories from grandmas/grandfathers. The way they narrated the stories through eye contact, facial movements, and signs using their hands, invariably made us read between the lines. During my kids' childhood days, I made them read a book (both Tamil and English) mostly with pictures often aloud, not bothered about the mistakes. So that they could be able to learn the vocabulary, and pronunciation, and speak fluently too. Reading should always be made as a gift to children but not as a chore. Children have become readers on the laps of either the mother or the father.
In schools, the teacher should let each student read a paragraph during teaching sessions and it must be noted that every student should be given a chance. As you said, school management may include projects for pupils to present a summary of a book of the genre they like every month to add internal marks for academics. During library hours, teachers themselves make it a habit of reading a book restricting gadgets inside the library or classroom. The schools or teachers arrange library visits and parents make a visit to book fairs for children and get them some audiobooks as well for a change. Let them know the importance of reading books for learning and make them knowledgeable. The more they read the more they learn. The more they learn the more they explore the world. To end with a quote, "A reader lives a thousand lives before s/he dies."