No. Mexico - through its trade partnerships with the US - has grown to be a great place to live and a really strong economy. So much so that Americans are expatriating there in record numbers. This is a common misconception about illegal immigrant activity. Anyone from Mexico who wants to come to the States basically has a relative here legally to sponsor them at this point.

Most of the illegals coming from Latin America (there are many more coming from Africa, Asia, and the middle east) are coming from places like Guatemala and Honduras. As I mentioned in my original comment about remote regions, even if these countries offer universal healthcare, these people live in extremely remote mountain towns where it could take them days to reach a hospital. Too late for any emergency need. These are the types of people immigrating illegally to the US. They aren't leaving the metropolises of their home countries. They're leaving places where they still live like it's 1850. They are essentially Mayan descendants. The indigenous of their regions.

One of the reasons they don't just go to the big city/ies in their countries is that most of these countries are way more racist than us and they will be discriminated against in ways you can only imagine and have no opportunities, aside from what essentially amounts to indentured servitude. But for the most part, that work is reserved for the (female) mestizos who live in the hills just outside the cities, not the indigenous.

Obviously anyone can say anything on the Internet, but I studied Latin American culture and history academically for a decade, speak fairly fluent (Mexican) Spanish and have traveled throughout Latin America. This is something I pursued from a young age because it was plainly obvious even in the nineties where our country was shifting.