Why is purification (Taharah) studied before prayer (Salah) in classical Hanafi Fiqh manuals?

Introduction to Kitab al-Salah: Scope and Study Method

• Because prayer is voluntary while purification is always obligatory.
• Because ritual and physical purity is a mandatory prerequisite (Shart) for prayer, and a condition logically precedes the act itself.
• Because purification is longer to study than prayer.
• Because the author wrote them in alphabetical order.