For one court to come to this conclusion and then enforce a large scale national policy shift, even temporarily in the case of the ruling being over turned by a higher court, is a pretty jarring exercise of power by an unelected official over an elected one.

Of course, if it is confirmed illegal by higher courts, then it is with in the checks and balances to order civil servants to stop collecting the tariffs even if the White House orders them to keep doing it.

There are of course situations, particularly concerning the violation of people’s civil liberties, where such a halt order is entirely warranted even if it is jarring. But the White House abusing a vague power to collect additional taxes on imports, while harmful and disruptive, is not as directly harmful or destructive as people getting black bagged or having their citizenship revoked, where a an order to stop from a lower level judge until the policy is reviewed at a higher level, is entirely warranted.

Staying an order pending judicial review isn't uncommon, particularly if it's on matters far beyond the influence of that court.

That said, it's not like this admin cares what any court says anyhow. The scotus could say in plain as day language 'no you for sure can not do that' and it'd get brushed off as irrelevant somehow.

Schroedinger's illegality.

Courts do not control the police. Or army.

As far as a president is concerned. Congress followed by the Senate. Is the only organisation with any ability to control him.

And the US has seen. They have to be politically willing at both houses to have any effect.