What’s the catch with the Apple Upgrade program?

Apple's new Upgrade program is here, allowing you to lease select models of iPhones, iPads, Macs, and Watches with a relatively low monthly payment. The company promises you won't pay more than the full price of the device over the course of the one- to three-year lease, and in some cases, you'll pay hundreds of dollars less. The basics of the program make it sound like an amazing deal… so surely there must be a catch, right?