For example, it would make it harder for the human traffickers to entice people to hand over their life savings only to be dropped off in the Arizona desert with no water, after their daughters were raped.
As far as a crisis for American citizens, it could be argued that: (1) every person coming across takes away a job from an American citizen, putting them and their family at risk, (2) every person coming across is likely to collect some sort of government benefit (and the Dems are very worried about deficit spending right now), (3) every person coming across without being vetted is a security risk (why wouldn't terror groups send people over via Mexico to do what that guy in NZ did?). I'm sure other reasons could be offered.
I'm not trying to argue the substance as much as I am pointing out that these issues are judgment calls. Granted, an activist court could decide to substitute their judgment for the judgment of elected officials in Congress and of the president, but they are not supposed to do that. We have elected officials to make these types of non-courtroom judgment calls. Congress gave an ambiguous power to the president, which means the president can use his discretion to flesh out that ambiguity. Count your blessings: the next Dem president is going to have a field day with this.
Personally, I would rather that any president, whether D or R, did not have this power. My best scenario would have been a unanimous Congress shutting Trump (and all future presidents) down for good by rescinding this law. Do you agree?