Who would pass such a law? Hell, who would even vote for such a law? Churches have enormous influence at the ballot box.
Even at the peak of its power, the Soviets couldn't simply abolish religious leadership. And they were in a country with Atheists in the highest tiers of government, with actual money and military power to toss around. What's the plan to outlaw religious demagogues in a state founded by religious demagogues?
On one hand, yeah non-religious is what I want to happen in our government positions. But on the other hand, making it a law is one of those things you just can’t do.