You're thinking about the state of the economy today and yesterday. Maybe you're only thinking about people who grew up south of the southern border. Low skill immigrants come from many places. Many pay lots of money to get here, if they don't see a market for their low skills, there is no reason to come here. Low hanging fruit [low skills jobs] are being replaced by automation, slowly, but it's on its way. Currently there is a net negative low skills immigrant flow. As automation accelerates, it's likely to increase low skills immigrant outflows. Conversely, we may see more net inflows of mid and high skills immigrants.

And, as minimum wages go up, high school graduates become more willing to work. At $10 you may not find manual labor worthwhile, but at $15 it looks more enticing. Now, immigrants typically work a little harder, but not so much to overcome a lack of education and poor communication skills --which can take years to develop if Eng is not their native lang.

As tech advances and "hollows out" low skilled labor from advanced economies, these economies will struggle to keep their mid skills labor market employed.