The wall has already done "something".
From the first link in the OP:
Data released by Customs and Border Protection in July show that illegal border crossings fell to their lowest level in June, with no parole releases of illegal immigrants.
There were 25,228 total encounters nationwide in June, down from 29,478 in May, marking the lowest monthly total ever recorded by Customs and Border Protection, the agency stated.
Border Patrol apprehensions nationwide also dropped to a historic low, with 8,024 apprehensions recorded, compared with 10,357 in May, according to the agency.