I've expressed on this for some time.
And just as a point of comparison, even in the Old Testament at the very beginning of Israel's post-Exodus existence as a nation, you find a distinction between "church" (the Aaronic-level priesthood) and "state" (Aaron's brother Moses). And of course, later civil leaders were not necessarily even Levites, let alone Aaronites. The two were connected, yet one could separate them.
