It's not a different discussion. The Constitution has not worked to restrain the govt from violating the rights of the people. The state works with impunity in its endless foreign and domestic wars, it wastes resources on pet projects, and it destroys any notion of "rights" via personal behavior prohibitions, eminent domain, and taxation.
Your "natural rights" wouldn't be supported for free in a stateless society. But they aren't supported for free now. You have to pay exorbitant amounts for sub-par service, to enforce "rights" that you don't necessarily agree with.
But your rights would be supported in a responsive manner by voluntarily funded, efficient institutions that care about the well being of their subscribers. You would get the best price for the best service, or you could switch providers.
Sounds better than enormous prices for the crappiest service imaginable and a prohibition of switching providers!