Nothing, and that is my point.
While it is fun to point out that both District Judge Robart and the Three Stooges of the Ninth Circuit are dumbasses who haven't kept current (there have been at least three terrorist incidents or arrests involving immigrants from the "Maleficent Seven" that we know of. No doubt the FBI has thwarted more.) But entertainment value aside, both Robart and the Nutsy Nine have made a big deal out of the fact that Trump's argument doesn't cite any people from these countries committing terrorist acts.
They're laughably mistaken, but it is irrelevant and dangerous to the legal question.
The judiciary aren't entitled to proof that a law, EO, or even a policy position taken by the lowest bureaucrat in the bowels of an obscure office building in the hinterlands will actually achieve a stated purpose. To act as if they had such a review over political decisions is fatal to government of, by, and for The People.
Everything you say makes perfect sense and you state the case with admirable clarity but surely what the court decided was not that the EO was wrong or misguided, it merely said that the government had not shown enough reason why the temporary ban on the implementation of the EO imposed by the Washington court should be lifted.
For the government to get a ruling overthrown and not simply wait until the lawfulness of the EO was tested in the lower court it had to prove there is an urgent need to reinstate the ban and that is the nub, they could not do so and the court upheld the temporary stay on implementation.
If you want to get a court to override a stay of execution until such time as the court gets to try a case you need to show there is an emergency.
If one listened to the squawking of the media you would be led to believe that the court had ruled the EO to be unconstitutional, it did no such thing, it simply upheld the suspension of the implementation of the ban imposed by the lower case until the legality or otherwise of the EO could be heard in that court.
I entirely agree that the ruling displayed shocking judicial over-reach but in no way did it somehow declare the EO to be unlawful or illegal, that issue has not yet been heard in a court of law.