---No solution is perfect. But a wall/fence makes a lot more sense than nothing at all. And it will not cost anywhere close to half a trillion dollars nor take 20 years to build. And I'll bet you know that. ---
It worked well for Hadrian and the Romans in northern Britain. They put one up there not to deter an armed invasion but to regulate the flow of goods and people on a frontier too long and rugged to patrol effectively.
We only have 12,000 border patrol agents total. By contrast there are almost 40,000 officers in the NYPD alone.
And NYC is as safe as the Vatican.