To be cogent, one has to be logical and clear; therefore, flawed logic is absence of cogency by definition.
There is nothing non-cogent with arguments in defense of the free exercise clause of the First Amendment, or in defense of the free market versus government-micromanaged economy.
You appear to be mistaking flowery oration for cogency.
Some of these arguments appear cogent because they are simply stated and follow logically from the starting propositions.
I agree with spintreebob that if people don't recognize that there is more to the economic debate than capitalism vs. socialism they are necessarily starting from faulty propositions, and any argument they make no matter how valid will lead to a wrong conclusion.