It’s not that border control has been tried and failed; it hasn’t been tried. Thanks to court decrees and congressional enactments, we don’t permit ourselves to quickly return minors from Central American countries, or to detain them for any significant period of time. They get released, along with the adults accompanying them.
The asylum process is broken. The initial so-called credible-fear interview to determine whether asylum-seekers get to the next step of the process approves almost all of them, even if they are unlikely ultimately to win asylum. In the meantime, they are waved into the country and probably never removed.
The migrants coming in increasing numbers realize that we are helpless to exclude them and, indeed, surrender to Border Patrol agents when they get here.
Congress could fix all this in an afternoon, with a few key changes in the law.