McALLEN, Tex. — President Trump traveled to the Rio Grande Valley earlier this month and made his case for building a wall on the Southern border — needed, he said, to keep America safe from a variety of dangers that are continuing to make their way across the frontier from Mexico.

To help make his point, the evidence was laid out on tables: a big bag of cash, bundles of drugs, high-powered firearms, all confiscated by law enforcement agents working the borderlands in South Texas.

“This is just all recent. This is all very recent,” Mr. Trump said, pointing to the illicit exhibit in front of him. Mr. Trump was not shy about his disgust for the illegal goods: “It looks pretty brutal. This is not a manufactured deal, as you say. This is the real stuff.”

But the display at the president’s Jan. 10 round table, it turns out, had little to do with what happens along unfortified reaches of the border. An examination of the seized items suggests that a border wall would not have stopped most of the items from entering the United States, or, in the case of several weapons displayed in front of the president, from leaving the United States for Mexico.