Do we really want a religious government?

I got to thinking about how the voting republicans all want religion to be part of government (now i mention voting republicans and now all republicans). I got to thinking in depth about this, mostly because I've been reading a bit about Buddhism, and how different it's religion had effected government.
As a religious leader looking not necessarily for power but a way to maintain it, a religious backing is the best way. A government that creates law and policy under the preface that it is gods doing or gods work creates a very powerful system. In that anyone who questions the law or policy questions god, and thus they are deemed heretics and not taken seriously. The leaders also remove responsibility from their shoulders. This is because if they laws and policy are the will of god then the outcome of these laws and policies are the responsibility of god, not the politicians. As well they create an unquestionable system, as if the policy and laws are the will of god, you have to take up anyway questions, praise, or qualms to god. And the last I heard (or not heard) was that god has not been answering to questions for quite some time.
So for anyone out there looking to create a question proof government, religion is the way to go. But for our leaders of a democratic government this is atrocity if committed is to be with out forgiveness.

Cheers
Zachary