The intention was that the secular church (IE the pope) would have no authority. The laws and morals of the nations are most definitely Christian based. You can't have a government separate from Christianity in the west, because Christianity is such a part of the culture and people make up a government ergo, it gets in. It would be nice if policy was based on rational thought but this is most definitely not the case as seen in the case of abortion, gay marriage, taxes(socialism isn't rational), healthcare(keeping old people alive so they can live but not work isn't rational) oh, most things. We do them because we're culturally set up to. Think about all teh trouble politicians get into with adultery. Would a rational government care about that sort of thing?
Oh and the best interest of the people? That is funny how rarely the government manages it.
We'd like to think we're separate from religion, while what we actually are is mostly separate from the churches.