Should the US treat visitors with respect and make the process of entering and leaving predictable and transparent? Yes. But saying foreigners have due process rights goes beyond should into must. And that is incompatible with our traditional views of sovereignty.
Except the Supreme Court has upheld various rights foreigners have w/r/t the bill of rights.
See in particular his quote from Scalia's dissent in Boumediene:
“The alien, to whom the United States has been traditionally hospitable, has been accorded a generous and ascending scale of rights as he increases his identity with our society . . . .
“But, in extending constitutional protections beyond the citizenry, the Court has been at pains to point out that it was the alien’s presence within its territorial jurisdiction that gave the Judiciary power to act.” Id., at 770–771.
Not even Glen Greenwald claims that the U.S. Constitution applies to non-citizens trying to board a plane in Cairo.
[1] Though many people would say it's a separation of powers violation.
You're always playing a bit of a lottery whenever you interact with, well, just about anything. But when domestic police screw up (or not!) and you get in trouble, there's at least a process in place that tries to smooth things out. It's still not a guarantee, but if you didn't actually do anything wrong, the process makes a decent stab at ensuring that fact comes to light.
But start crossing a border and everything changes. A single wage slave having a bad day can ruin you. Low-level consulate worker decided you screwed something up, even though you think you didn't? Well, too bad. Go find another country to live in.
For whatever reason, we completely throw out all these principles the moment we look at people crossing a border. And worse, everyone thinks this is fine. Foreigners have to rights, and people seem to think that's how it should be.