Ruling by religion, was tried in the United States and it failed-miserably. Here, for example, is an early colonial law:

If any man have a stubborn or rebellious Son, of sufficient understanding and years, viz. fifteen years of age, which will not obey the voice of his Father, or the voice of his Mother, and that when they have chastened him, will not hearken unto them; then shall his Father or Mother, being his natural Parents, lay hold on him, and bring him to the Magistrates assembled in Court, and testify unto them, that their Son is Stubborn and Rebellious, and will not obey their voice and chastisement, but lives in sundry notorious Crimes, such a son shall be put to death.
The law then states the specific biblical chapter and verse on which the law was based (Deuteronomy 21:18-21).
If a man have a stubborn and rebellious son, which will not obey the voice of his father, or the voice of his mother, and that, when they have chastened him, will not hearken unto them: Then shall his father and his mother lay hold on him, and bring him out unto the elders of his city, and unto the gate of his place; And they shall say unto the elders of his city, This our son is stubborn and rebellious, he will not obey our voice; he is a glutton, and a drunkard. And all the men of his city shall stone him with stones, that he die.
How many of us would be alive today if that law were still on the books?

Source: Ain't Nobody's Business If You Do: The Absurdity of Consensual Crimes In Our Free Country