Problem: politicians have families. Unless becoming a "government citizen" propagates recursively to cover one's extended family, and perhaps their extended families as well, i.e. potentially hundreds of people in total, there's no way to isolate the new member of government from having incentive to help their loved ones, who are still "commercial citizens".

Conversely, if you somehow solve that, it brings forth a new problem: the "govenrment citizens" are now an alien society, with little understanding of lives of people they serve. To borrow your priest analogy, it's like Catholic priests giving marital advice to couples - it tends to be wildly off mark, as celibacy gives the priest neither experience nor stake in happy marriages.