de facto perspective: can, can't
The government shouldn't do what they are doing. But they can, and they do.
State governments can still take power away by convening a Convention to Amend the Constitution and then ratifying a Constitutional Amendment.
And of course the government can and does give itself authority. All authority of the United States government even at the most fundamental and historic level comes from, well, itself. The very foundation of the government comes from the government deciding what counts as “consent of the governed,” obtaining that level of consent, then going forward with all the authority it decided to grant itself.
If the South wall is put into place, it might be possible to justify reducing the margin in which they can conduct searches without warrant, but at the moment it's a crucial tool both practically and in the minds of those charged with defending the border.
Sadly, a considerable number of people in the U.S. are dead set against the wall, and don't understand that the requirement for ladders and climbing makes non-customs crossings more conspicuous and time-consuming, making unpredictable and regular patrols considerably more effective whether or not the wall proves to be a total impasse.
https://www.aclu.org/other/constitution-100-mile-border-zone
I did not make that argument, sorry if I wasn't clear enough.
YIKES.
https://mitpress.mit.edu/books/walled-states-waning-sovereig...
Because some specific threats, specifically to sovereignty, can be deterred, retarded, and/or prevented by a wall.
From the link, emphasis mine:
"Our lawsuit, filed in September 2017 on behalf of 11 Americans whose devices were searched, takes direct aim at the illegal policies enforced by the U.S. Department of Homeland Security and its component agencies, U.S. Customs and Border Protection (CBP) and U.S. Immigration and Customs Enforcement (ICE). In our brief we explain that warrantless searches of electronic devices at the border violate the First and Fourth Amendments, and that our 11 clients have every right to bring this case."
The EFF is filing suit because they believe the government has broken the law. If the government had not broken the law but the EFF desired to change the governments power then they would lobby congress.