Hmmm. You'd have to displace a whole lot of Mexicans, turning them into the Palestinians of the 21st century. I remain skeptical, but open to good arguments why we would want those 200 miles of Mexican territory (since as far as I'm concerned it's all ours lent to them on sufferance after the Mexican War).
Well, argument #1 is yours-it's our land, we won it fair and square.
Second, a line 200 miles to the south is shorter and the construction of the necessary wall will be easier (I obviously haven't done the survey, just where the most fortifiable line is is subject to debate).
Third, a destabilized rump Mexico, like the West Bank, will be unable to resist necessary punitive expeditions and search and destroy missions looking for terrorists. We will need several divisions of former Mexican citizens to work with us on this, my sense is that Sonorans and Chihuauans are better candidates for this role than peasants from the South.
The main point is that I think globalization will fail (has indeed failed already), that we need to plan for Fortress America, and that Mexico and Canada as presently constituted could become more threatening than the rump beggar states they could be turned into.