It wasn't herds of cattle moving through the jungles of Central America that likely helped the screwworm breach the barrier we'd been maintaining for decades. It was mass human migration. Once they managed to move north any animal was a potential host, not just commercial critters.

And even then it probably could've been held at bay and fought back south, except Mexico in particular was extremely sensitive about any suggestion they might not have everything completely under control.

Even so, the US started contingency plans a while ago just in case, and construction of the new facility. The comments here are quick to try to take a jab at the government but short of nuking southern Mexico from sea to glowing sea once the screwworms breached the line, and that breach wasn't US territory, don't know how this was ever going to play out differently unless the locals at every step of the way stepped up.