"I see no situation in which extra-judicial deportation (or extradition!) is the right course of action."
I see one: where the country in which the crime was committed (the "deporting country") considers spending resources to prosecute the offender, indulging him with a court process (including trial and appeal), and then housing and feeding him during his sentence (if he is jailed) not in its public interest.
I say "indulging" because due process is expensive. Why should the deporting country be obliged to spend their taxpayers' resources on this foreign national? Not because deporting their national back to their home country would create "disorder and enemies" due to the harm that such "rattlesnakes" would do in its territory, since (1) that home country would likely welcome the discretion to decide how to deal with its national committing crimes in its territory, (2) it is not likely that the home country would protest that its national was not sufficiently punished by the legal system of another country unaccountable to it and outside its jurisdiction, and (3) in some circumstances the home country can still exercise extraterritorial jurisdiction over its national for the crime he committed overseas. The prosecutorial discretion of the deporting country should not be fettered by the home country.
How do you know that the person is even a foreign national? Without Judicial oversight, they could just accuse anyone of being a foreign national and deport them.
This is exactly how disappear people, and start a reign of terror.
I see one: where the country in which the crime was committed (the "deporting country") considers spending resources to prosecute the offender, indulging him with a court process (including trial and appeal), and then housing and feeding him during his sentence (if he is jailed) not in its public interest.
I say "indulging" because due process is expensive. Why should the deporting country be obliged to spend their taxpayers' resources on this foreign national? Not because deporting their national back to their home country would create "disorder and enemies" due to the harm that such "rattlesnakes" would do in its territory, since (1) that home country would likely welcome the discretion to decide how to deal with its national committing crimes in its territory, (2) it is not likely that the home country would protest that its national was not sufficiently punished by the legal system of another country unaccountable to it and outside its jurisdiction, and (3) in some circumstances the home country can still exercise extraterritorial jurisdiction over its national for the crime he committed overseas. The prosecutorial discretion of the deporting country should not be fettered by the home country.