Even that depends. If they pick up some guy who is already flagged for deportation because they know he's not a citizen, they don't need to show anything to a judge.

This is not about whether a judicial review is required - it's about whether it is available when invoked.

If they pick up a guy that they believe is flagged for deportation - even someone who their claim is subject to a removal order - that person still has a right to request judicial review of his potential deportation. The government could be making a mistake: they might have the wrong person, and the individual isn't subject to a removal order. The removal order might have been revoked or suspended, and there's a mistake in believing it's still in effect. The removal order might have been superseded by another action - there's a lot of DACA recipients who were subject to removal orders as an entire family when they came over as children, but those orders are suspended by DACA. Etc.

The problem here is much worse than if the Administration did not on its own go into court - because as you point out there are situations where the the government is no longer required to go through a judicial process. The problem is that the individuals had sought judicial review, and the judge was considering the case and had allegedly told the government not to remove them from the country while that was ongoing; and the Administration is making noises that even then their actions are not subject to review. That they can just disappear someone from the country and that person is utterly beyond the reach of the courts - even to argue mistaken identity, even to argue that they are in fact here legally, even to argue that some other provision of law prevents their deportation. And that's just a terrifying degree of immunity from the rule of law for the government to claim that they have.