And for what purpose do they control seek to control these borders? Why is a North Korean or East German border what seem people prefer for the U.S.? Fences work both ways, you know...
Freedom of movement by the citizens within the country is a whole other ballgame.
The lines being crossed are imaginary in both instances. If the Governor of New York declared he wasn't accepting immigrants from Mississippi or Alabama, and needed to put a tax on goods from those areas in the name of preserving jobs (creating goods that are made cheaper in MS or AL), would it be a good idea? Why or why not?
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a thousand answers to this question including the need for population control and the welfare state which will never be repealed, but the one that comes to mind more than anything is national security.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.