Upon what Constitutional basis does the Court claim to have the right to tell private industry who to hire and who to fire? I can find no such proviso in the Constitution or any of its Articles.
Leaving aside the fact that this us a State law, and the States generally have more leeway to do things unless Congress has used its delegated powers. The Congress has plenty of power to this itself.
Congress thus has power to control immigration. Furthermore, Congress has the express power to prohibit certain people from immigrating.
The only way the Arizona law could have fallen afoul of the Constitution would have been if the Court found that Congress had legislated in a manner that precluded State action, and the Court found that this particular law did not run into a Congressional barrier. Thankfully, the Court exercised some common sense and restraint here.