“We’re almost literally sucking Mexico’s brains out, leaving mostly the dregs”
More likely we are achieving the exact opposite, taking the least educated and least skilled. While it is hard not to admire the guts and determination of illegal border crossers, in an information-age economy it is mental prowess not physical strength that determines a nation's fitness.
“'Free market competition' ...”
Allowing the labor market to be flooded with unskilled labor is a protectionist measure; it benefits certain industries and groups at the expense of others. In effect it alters free-market conditions that would exist within our borders (assuming you believe in borders).
After sending my earlier post I came upon http://msnbc.msn.com/id/12248887/ (title: "Mexicans join tech force"), which details the small but growing group of Mexican immigrants who write software for Microsoft.
No doubt they are a very small portion of Mexican immigration and are (I presume) legal but an interesting counterpoint to the usual images of various immigrant groups.