Several side-effects result from requiring peer review. First, by setting the peer-review deadline at least one week before the assignment due date, students spend more time thinking about and revising their drafts. Not all students will have complete drafts at the peer-review session, but far fewer students will put off any work on the draft until the night before it's due.
Second, requiring peer review guarantees that at least one other person has read through the draft. Granted, students can ignore all the advice peer reviewers give them, but most will ask for yet another opinion if a peer reviewer says that the draft is completely off track or incomprehensible.
Third, but not least important, when students read each other's drafts, they get yet another chance to see a different approach to the assignment and to think through the key criteria for the assignment. Often a question on a peer review worksheet will trigger new thinking about a student's own draft after commenting on that point on the peer's draft.