Snake Oil and Border Security

I have been trying to avoid spending any time thinking about politics, economics and the current state of things in the United States. Despite my sincere effort, I keep drifting back into the morass of commentators and politicians. It makes me wonder about how any of us can distinguish the true from the fake, the actual from snake oil.
My thought process seems to be more than random but less than objective. I am somehow pulled and pushed in ways that are confusing and hard to track. The border with Mexico is a prime example. Is it merely a boundary between two countries, the door to opportunity for many of our southern neighbors, the dividing line between us and them or the entry portal for criminals and hooligans? My rational self thinks the border is a mix of all of these. The political jousting tends to focus on the criminals and hooligans, of which there are certainly some. Nearly everyone agrees that keeping them out is a very good idea. We definitely do not want more criminals and hooligans to add to the home-grown variety we already have.
According to the Google guy, the US Mexico border is just short of two thousand miles. It's about the same as the distance from Cleveland in Ohio to Las Vegas in Nevada; or about the same as from Chicago to Los Angeles. With that perspective, imagine building and maintaining a thirty-foot-high wall or a shorter fence for the full two thousand miles. Additionally, you need to make sure no one breaches the barrier.
President Trump and those on Team Trump tell us that the only way to keep the criminals and hooligans out is to build and maintain the two-thousand-mile wall. Our fear of the invading criminals and hooligans should be a sufficient motivation to build it now. The opposition team tells us that there are better and less expensive ways of keeping the criminals and hooligans out, although so far, I haven't heard much about what those better and less expensive ways are. They seem to have something to do with electronics and drones.
My rational self tells me that either approach would probably work equally well. Either the old-style wall or the new-style technology would likely stop most but not all of the illegal border crossing. Either would be particularly effective at stopping children and families. The real issue is how well either would be at stopping criminals and hooligans. I suspect either approach would slow down the influx of criminals and hooligans but many if not most determined criminals and hooligans would be up to the challenge of either type of barrier. I doubt that either approach would actually reduce the number of criminals and hooligans all that much who get from there to here. Even so, either approach would likely reduce the number of good people looking for a better life who make the passage.
There is another confusing element in all of this. How many people currently cross the border illegally each year? It matters since that is the number that either the President's wall or the oppositions technology is expected to reduce. I haven't heard even an estimate of how many. Further, I haven't heard how much reduction we should expect using either people stopping approach. Focusing specifically on criminals and hooligans, how many bad people illegally cross the border each year and how much will that number reduce by way of the wall or advanced technology?
For the business people among us, let's think about this. the current border security has been working fairly well for quite some time. Most but certainly not all illegal border crossing is already being prevented. Without any border security, let's say that the number of criminals and hooligans crossing the border illegally would be X. With the current security Y criminals and hooligans are prevented from crossing illegally. The number still crossing is then X minus Y criminals and hooligans. Let's call that Z criminals and hooligans. The value of the wall or the technology is thus how much reduction the...