Hi there. I'm a first-year PhD student in public policy.
I will be obtaining an MPP once I finish my field exams en route to my PhD, but I applied to my PhD program directly. Several of my fellow PhD students already have MPP or MPA degrees from other programs, but they have not been able to waive their core PhD requirements. Instead, they've chosen to take all of the core classes at the doctoral level -- so some material is repetitive, but a lot of it is taught at a higher level -- or they've opted to take a few PhD classes from other departments on campus (such as the economics department).
If you would like to work toward a PhD in public policy, you would want to apply to PhD programs directly after finishing your MPP. That means more time spent in school, but there are benefits to getting the MPP first; it would show admissions committees that you're serious about public policy (especially if you do very well in the MPP program) AND it would give you a good amount of background heading into a PhD program.
I hope that is helpful!