https://en.wikipedia.org/wiki/Israeli_West_Bank_barrier
They use a 200 ft exclusion zone where possible.
Without an exclusion zone, multiple swarms can overwhelm the system.
Probably not much of a tactical gain, but a strategic gain; massively increasing US manpower requirements.
Definitely, a multiple barrier system (a wall and fence, or two or more fences), with an alarmed exclusion area between them is the biggest force multiplier.
A big wall will screen out the bulk of border crossers, so there would be fewer cases to focus on. With the crowds deterred, the cartel smugglers will stand out all the more, for greater focus.
Sensors and cameras in the exclusion area can collect evidence 24x7, to quickly identify new methods smugglers are using.
I would also like to see every patrol vehicle equipped with an aerial drone or two. Border Patrol wants a see through fence to keep an eye on what is happening on the South side, but it allows the bad guys to constantly monitor the Border Patrol’s movements as well. A solid wall, with air supremacy for the Border Patrol would be the best of both worlds.
Drones would also allow officers to constantly track border crossers, until they can arrive on scene to arrest them.