The question has no basis to begin with because states cannot set up their own immigration policies, that is left to Congress. Technically I would imagine Congress would have the right to control people's movement between states, but that is not politically realistic or feasible.
And for what purpose do they control seek to control these borders?
There's a thousand answers to this question including the need for population control and the welfare state which will never be repealed, but the one that comes to mind more than anything is national security. There are bad people out there who don't like us and do not need importing.
You're dodging. I didn't ask if it was popular or even feasible (locking down the U.S. like East Berlin isn't feasible either). Just whether or not it's a good idea to restrict immigration from low income states with low unemployment to high income states with higher unemployment. So what do you think, good idea, or not?
There's a thousand answers to this question including the need for population control
Population control? You think the government should regulate how many babies people have? You're starting to sound like a statist, not a Reaganite. Who are the busybody bureaucrats that know how much population the U.S. 'should' have at any given time?
and the welfare state which will never be repealed,
Ah, finally we hit upon the real enemy. Stay focused on socialism, not immigration, because it's the real enemy. The welfare state isn't eternal, it's self defeating.
the one that comes to mind more than anything is national security. There are bad people out there who don't like us and do not need importing.
They can walk from Afghanistan to Pakistan, but a trek through the Canadian woods or the Mexican desert is too tough? If you think the U.S. federal government, or any other entity, can 'secure' the borders you've been duped.