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What does every single person who cross the US border illegally have in common? Answer: The first act upon reaching their new county is to piss all over its laws.
The problem is, there aren't illegal. Mike says he now cringes every time he hears them described as "illegal" because he knows they aren't.
It's a different process than Ellis Island, at least somewhat. But it's entirely legal.
Every other one of your points is either false (e.g. non-citizens cannot vote in Arizona), or will be struck down by the courts. No matter who wins next year, the border cannot (and will not) change without legislative action. It's how our laws, and our Constitution, work. Or don't work, depending on your point of view. We are not yet an authoritarian state, so decrees from the Executive can't fix this problem.