Thus their departure would raise incomes in Mexico while lowering it in the US. So your point is mostly right, at least as it relates to this story.
NAFTA fucked rural Mexico as a tidal wave of cheap corn flooded the economy and killed the smaller scale agriculture, just as it did in the US. You also have periods where economic crisis and monetary devaluation in Mexico wipes out a lot of middle class type people. A lot of laborers and construction guys came because of this.
You also have an insurgency in many parts of Mexico where the cartels have taken over and often little functional government exists. People there bug out if they can.
Many of the "peasant" immigrants are from Central America and pass through Mexico.
As far as economic impact, it's a complicated issue there too. The big land interests in Western States generally control the senate delegations pretty tightly. A lot of people are making a lot of money off of illegals, so if there were some major change, you'd see some sort of guest worker visa or change to labor laws (especially minimum wage, workers compensation and overtime) to keep the farms picked and slaughterhouses running.
One of the most obvious examples of this - for generations, health care professionals in low-development nations have been emigrating, seeking higher incomes in the developed world. That's despite the fact that they're almost always middle class or higher in their own country. You could see this in action over the last 50 years across poor nations in Asia, Eastern Europe and Latin America. Currently the middle class is flooding out of various poor Eastern European nations, seeking a better life in eg Britain.
There were about a dozen articles posted on HN about this concept when the Syrian refugee crisis was peaking.
The doctors, etc are a minority. A visible minority, because their move harms their country of origin more than a loss of a builder from a social perspective but still a minority.
Increased wealth and better access to information and information technology in African and Asian countries is what's pushed the recent migration towards Europe (via Turkey, Libya or Morocco) on the move.
I don't think that is a good argument, since once they move to the US they would be making middle class wages in the US, since they have the relevant skills to be employed in middle class jobs.