Going into more detail on what I hope to accomplish with a doctor Primarch.
There's a lot of places a superhuman medical expert would be useful, removing the Butcher's Nails would be one major example, as would curing the Red Thirst for Sanguinius. We might even be asked to help with the Flesh Change depending on when we're found relative to the other Primarchs, which would open up some sorcery-based plotlines, as we learn what affects the soul can have on the body and vis-versa.
We'd probably have the Rangdan as our most hated enemy, as most versions I've seen are effectively a sentient disease, though Nurgle would also be a contender if and when he shows up. Other possibilities include making biomechanical servitor replacements that don't include human tissue for ethical reasons, building a universal health care system for the Imperium, and removing the "death rate" for space marine conversion.