I believe we can use this distinction between two types of constitution, written and actual, to inform our discussion of whether it might be wise to write a constitution for a nation. We are painfully aware of organizations, such as the U.S.A., where the actual constitution differs from the written constitution. And from this experience we might infer that it is pointless to ever write a constitution for an organization. But we could. For your sake we will.
People sometimes hunger to know how an organization works.
We see a demand for information. Where success of an organization suggests that the organization must have a good actual constitution, people will demand copies of that constitution in writing. Yes, I think, within limits. A written constitution will change things to the extent that it shows people how they can actually advance their ends. Every organization will contain interests which possess, or which can assemble, power to change the actual constitution.