What country do you throw them to? I would assume no other country will accept criminals being tossed out of the country for a crime they committed. Interesting idea but it doesn't seem possible to enact.
A more than fair question.
America is the "World's Bread Basket" Our country delivers a massive amount of food aid to many parts of the world on a regular basis. Without these shipments, many places around the world would collapse.
Make it part and parcel to any nation accepting food aid from the United States. Simply add cells and temporary lock ups in these shipping vessels and do handoffs in international waters before the vessels reach dock in another country.
Non US citizens being handed off in international waters. Care/Custody/Control are all accounted for and built into existing logistics. Lots of lawyers in the forums, let's see any of them try to unpack this one.
The new "host" nation can decide what to do with these new "refugees" Some might try to rehabilitate them. Some might use them as labor in exchange for new citizenship. Honestly? In most cases, they'll be executed and tossed overboard out of the sight line of American cameras.
I'm talking career criminals, drug dealers, rapists, burglars, wife beaters and hardened felons. All given trials and all convicted. Would empty out our prisons. I've just given every teacher in America a raise. All that money saved ( it's about 75K a year and growing as the cost to house and secure a prisoner in the United States) can be used to actually help our society function better. How about a new library? An after school martial arts program?
It works. And it sells. I have a hard time seeing most Americans opposing a new library right after a bunch of convicted rapists get the boot. Someone will say no host country will want a bunch of entitled smug American rapists in their country. They would be right. And they would probably magically disappear before that vessel hit dock in a different country.
Add anyone who threatens to shoot up a school to that list. Give them a trial and if they are convicted, strip them of citizenship and toss them out. Most of you are parents. Your teenager doesn't want to live by your rules? OK, pay your own bills and get out. See how good you have it here when you realize how cold brutal and dark the world really is out there. This is no different. Don't appreciate being an American? Get out. Don't appreciate being given the opportunity of being a young person in America who can get a real education ( compared to the rest of the entire world and across all of human history, the education that American children receive is incredible ), then get out.
The open threat of being thrown out of the country and being tossed to the wolves outside of the "Western Bubble" should be a fine deterrent.
Problem solved.