Music lessons are not primarily about learning a lot of pieces. Rather, they are about learning a sequence of skills. The skill must be taught by the teacher, not just read about in the book. (That’s what you’re paying me for!) The piece is there to reinforce and apply the new skills taught by the teacher. If the student attempts to learn the piece without having learned the skills, the piece has been wasted. It is extremely difficult to add those skills after the student has practiced the piece incorrectly for a week or two.
What to do instead:
If the student wants to do something extra, he or she should ask the teacher first. There are supplementary material at the end of each book. Go there first. If the student runs out of things to practice (really?), he or she should focus on polishing previously learned pieces.