I see your point but a constitutional republic, such as ours, relegates law making to the congress who represent the people. They could base their laws and implement them according to sharia.
Our Bill of Rights guarantees our freedoms and laws must conform to that.
Some people claim that Iran was duly elected and has a constitution. But I read that constitution and it gives primacy to Sharia. So no suprise there when the Mullahs took over. It was a set up from the get go.