The truth is America is unique. America is "special".
America isn't unique as a nation built/founded by immigrants, but that aspect of our heritage is very much part of what makes us a great nation. I think it'd be to our peril that we forsake it for fear of anything, yet that does appear to be what is happening.
Of course, our nation is not made better by admitting malfeasants, felons and misdemeanants; however, in the calculus that weighs the overall gains and losses, it's hard to say the gains don't outstrip the losses.
No, I tend to believe that the United States was rather unique in it's open border policy. At least for the first hundred years after the American Revolution. There can be no doubt, the borders were wide ass open prior to the Revolution. I admit, I come at this from a unique perspective. Take what happened in Colonial North Carolina.
Remember Blackbeard? Do you remember that the governor of North Carolina gave him a pardon and, for a while, old Blackbeard settled down and gave the legal life a shot. Hell, maybe you remember that the same governor gave all Blackbeard's pirates a pardon too. Actually, dozens of them did settle down in North Carolina and lived a life free from crime. But what no one seems to know is that the governor gave blanket amnesty to EVERYONE and ANYONE. Murdered somebody in Boston, no problem. Come to North Carolina. Running from your debts in Philadelphia. No problem, come on down to North Carolina. That's right, he threw open the borders and even offered protection from prosecution to criminals, pirates or otherwise, who agreed to settle in North Carolina.
A hundred years later, and after decimating Indian Wars, the foundation of the Revolution was laid, not in the Northeast. But in the War of Regulation right here in North Carolina. Not to mention the Mecklenburg Compact, now a mythical document. And of course there are the Overmountain Men, and the legendary North Carolina Militia, the foundation of Morgan's riflemen--many were the descendants of those that came more than a hundred years before.
But no bit of history tell the story of America's open borders and diversity better than our entry into the Great War, WWI. Part of it was diet, part of it was open spaces, but a big part of it was, being brutally honest, genetic diversity. Our soldiers were some big ass boys. Almost a foot taller than the average European. Heavier, more muscular, down right scary--read European descriptions from the time.