Ask Georgia's farmers
how that works. Moreover, ask Mitt Romney how open hostility to Latinos works.
You seem to believe this is a simple, black and white issue. It's not. There are a host of interests to be balanced - employers, fellow drivers, insurance companies, DMV workers (whom you apparently want to make into police), others in the labor market, the interests of the immigrants themselves, and more.
Have you ever been detained by the DMV? Ever seen anyone detained? Ever heard of anyone being detained? Do you think that once people are being detained by the newly-empowered DMV employees, that undocumented workers will continue to go there? Of course they won't -- thus the problem of unlicensed, uninsured drivers will certainly persist. Your proposed solution is far-fetched to begin with, and unworkable if it was ever tried.