@aidan,
You sentence, "If a child reads a lot . . ." holds the key to this problem.
I formerly lived in Winchester, MA, a suburb of Boston. Familial income was high and the two biggest employers of residents were Harvard and MIT. The school system was one of the top 10 in the state.
High school students were asked to read one book during the summer if they were in standard English classes and three if they were in honors. When I was in high school, we were expected to read six, no matter which track we were in.
Every August, during the week prior to the beginning of the school year, the library is crammed with parents, trying to find the required books for their kids. The local bookstore has already sold out of their copies, but only during that week.
One book? That's pathetic.