That is it in a nutshell. I am out of the business now but I can tell you that you will never eliminate the Mexicans in construction. I think the same is true for motels and restaurants. The only chokepoints that are controllable are welfare and citizenship.
The Mexicans that I worked with had little interest in citizenship. They wanted work and a paycheck. If citizenship was dangled in front of them who could blame them for grabbing onto it. If it were clear that they were guest workers, then they would be happy with that.
I haven't been in areas where there are huge numbers so I have to cock my eyebrow at that and take your word for what the conditions are. As for the social mores of some of them I will have to agree. The border is no place for the weak of stomach. I can tell you stories that will have you literally vomiting. But I can match them story for story with tales of underclass white or Indian atrocities to the sensibilities. We are privileged to live in a fantasy rose garden when unspeakable barbarity is just down the street.
There are limits to the government's ability to shape what we are. For better or worse this country will shape itself around realities. Those realities include Mexicans. We just need to treat them realistically.