You're proceeding with the assumption the government would lose in court, which is not the case in the vast majority of these injunctions.

Isn't a full and proper court case required to decide what you have just proclaimed outright?

Yes. Yes it is. Which is why district court judges should not be issuing nationwide injunctions.

not a lawyer, but I believe the process involves (a) deciding if there is a case at all to be argued, which is this case there clearly is, and (b) weighing the harm of letting the government send US citizens to Sudan or life in prison in El Salvador vs the harm that would be caused by preventing the government from doing that while the case is adjudicated - which seems to be nonexistent.

That last point is where we disagree. It takes many years for a case to wend its way through the courts. We're looking at a world where a relative handful of lower court justices can issue injunctions one after the other until it's impossible for the president to do his job.

There's only one court that has the authority to issue nationwide injunctions, and that's the Supreme Court.