The reason America has not, over the past half century, been able to solve the problem of illegal Mexican immigration, is quite simple.
The ruling class in America has not the slightest interest in solving the problem, because for them it's never been a problem. Having 11 million illegal immigrants working in America keeps the local workers "flexible," if you know what I mean.
Billy-Bob's Contracting might be able to do your landscaping with guys happy to work for min wage, but Pablo's Contracting can do it with guys who will work for even less!
That's why the class of Americans who hire landscapers have never had a problem with illegal immigration. It's not just landscapers, of course. It's the entire gamut of service trades from aluminum siding installers to roofers to plumbers who are happy to work for cash under the table.
I was having dinner with my dear octogenarian dad the other day when he pointed out that even forty years ago you could sit at the Texas-Mexico border and watch the illegals walk into the USA. No other country in the world permits such an obvious violation of its sovereignty.
Pre-Schengen Europe had far tighter border controls in place than the US ever had on the Mexican border. If Austria and Italy and Portugal could control their borders, the only reason the richest most powerful nation state in the history of history can't is because they're not really trying.
Because if they got serious about stemming the flow of illegals, all those donors to the two-party system would have to pay more for their landscapers and roofers. Not only that, but take 11 million illegals out of the work-force, and you'd soon have upward pressure on wages for American workers.
And that's something the plutocracy has absolutely no interest in.