First of all if rights are inalienable, government can't provide them, they can only violate them, suspend them or ignore them. They fail the first test of recognizing the rights if all individuals and they fail their purported purpose of "protecting rights" on a routine basis. The reason why is simple, they are the judges of the limits of their own power. The separation of powers is myth, much like the Easter Bunny.
The solution is readily apparent, don't empower an institution that regularly violates rights. Sometimes a given good or service is provided by them, that doesn't excuse the rest of their actions though. Also, this of course doesn't mean those services are impossible to provide in other ways, it simply means "they" don't permit it. The problem with empowering this institution is you, nor your so called representative has any way to disentangle any goods and services from the plethora of bads and dis services they also ahem "offer".
As far as being unconstitutional, the constitution is no great measure of anything, and can be interpreted any way that leviathan wants to. Cough cough slavery, Draft, interstate commerce clause etc. Polishing a turd will not get the best results, but flushing it will.