That's not how it's worked the last 20 years. The government has had *wide* latitude...but to your point, even Richard Reid the shoe bomber got a federal trial. But he wasn't an illegal alien...

Even the enemy combatants at Guantanamo - foreigners who never set foot in the U.S. - were found to be entitled to a modicum of judicial review. To have a judge look over their case and at least give basic habeas corpus review of the government's claims. Even without having entered the U.S., the mere fact of their detention under government controlled territory in Gitmo was enough to bring them within the outermost reaches of the Constitution:

en.wikipedia.org - Habeas corpus petitions of Guantanamo Bay detainees

The problem isn't whether the Administration is wrong about TdA or whether these are terrible people who ought to be deported under the INA. It's the claim that none of these people have any access to the courts at all. Someone always has to double-check the state when they're locking people up, so that when the government makes a mistake (and they always will make at least one mistake, nobody's perfect) there's a legal pathway to make that claim to a judge.