Guantanamo? Why not?

Because it's much more expensive to transport and detain the migrants there rather than in the United States. To do what Trump wants to do, ICE needs a ton more detention beds - because they need someplace to put the people they detain here in the U.S. But the reason those people are being detained, rather than being summarily deported under expedited removal, is because they have some legal entitlement to a hearing or other legal process prior to deportation.

So if you were interested in "government efficiency," you would detain the migrants someplace cheap and close to where they currently are - and close to where all the immigration courts and DOJ/ICE lawyers and files and evidence and everything is. Either you're going to have to fly all those people back to the U.S. for hearings (crazy expensive), or you're going to have to set up parallel immigration courts and administrative processing and staff lawyers and judges and a host of other civilian personnel in Guantanamo. If you even can - while Gitmo is subject to federal court review for habeas petitions, it's still a foreign country, and it's possible the government doesn't have the power to exercise the administrative judicial power outside the U.S. (heck, they might not even have the legal authority to move the detainees there, since they're not supposed to remove them from the U.S. prior to their immigration hearings). It's just going to give all those migrants more legal arguments and bites at the apple to challenge their detention and removal proceedings.

It's a weird thing for the Administration to consider - it will be more expensive, slower, and very vulnerable to being stopped altogether. Maybe they're doing it for the optics of starting to involve the military more into handling immigration matters....but apart from that, I can't see how this makes any sense at all.