I think you would probably not, because you know it would be a war zone within weeks, with the poorest and most desperate people from all around the world swarming to your small part of the world, bringing with them huge social issues.
People who have the wherewithal to move across the globe are not "the poorest and most desperate people from all around the world", they are the ones with the means to pay thousands of dollars to mafias because we have no better system to bring them in.
Why is "mass migration beats down the working class" not bad enough to warrant restricting it?
As for stability, you need to consider the benefits of having the best people from around the world in the jobs where their comparative advantage is greatest.