With the level of surveillance trained on the fencing around the Capitol, walls work.
In order for a wall spanning the southern border to work the way you want it to, there would need to be active surveillance along the entire length of it, around the clock. Assuming one person on guard per 100 yards, working a standard 8 hr shift, that would require 10,317,120 people. This is not counting the extra personnel needed stationed at points of entry, as supervisors, to serve on regular patrols, or as maintenance workers for equipment and for the wall itself. So in order to have a wall that works, it would take roughly 20 million people.
The entire US military has about 1.3 million active and 800k reservists.
Good luck making that math work.