I think that the DHSc program may have some benefits for the PA who is considering academia and/or administrative/political positions like program director or AAPA position, etc. Personally, I like the option.
The "Dr." part doesn't mean squat to me. No one would be, nor should they be, addressing me with that title in a clinical setting anyway because it would only lend itself to confusion. Patients would obviously think I am a physician, which (of course) I would not be. If you just use it like you would any other degree, it will facilitate your upward progression in the profession to whatever your end goal may be.