In reality, Mexico has a huge problem. The cartels have infiltrated every aspect of life, including politicians, law enforcement, and tourism. (It's easy to do when given the choice between "take our money or die.") Because of that, the two largest exports from Mexico are drugs and slaves. Most people work for the cartels in one way or another. If you get married and have children, you are given a choice ten years later -- sell your children or let them work for the cartels. Sure, you don't have to go for either choice. "Free will" and all, but if you don't, then you get the other choice. At the end of that choice is murder. Things happen before that. And understand, your entire family is murdered.
Also, understand that the country Mexicans export to is the US. Those street gangs you might hear about on TV? They are the children given over to the cartels who weren't sold as slaves. (Sex slaves and free children labor? That's the kids who were sold.) They're also the ones selling the drugs and slaves. America is the chief buyer of what Mexico sells.
Now, what would you do if you were a Mexican?
And, tell me again, how does giving them free healthcare or even free money help them?