Plenty of legals do that kind of work as well. You gonna profile Mexicans? Might get my wife sucked in - she's fourth generation American, but ethnically hispanic. Speaks English just fine, but how do you tell she's American?
Illegals are here only because they can find a job and no one bothers them. As soon as their life becomes more difficult, they'll ask for a free ticket back to their home countries. The troublemakers need to be arrested and deported.
You really think they are gonna be in any hurry to go back to their hellholes at home? Hard times in the United States is still a lot better than good times in the mother country...
Her employer must ascertain that. Now employers aren't obligated to make sure that the documents presented by an employee aren't fake, while DMV offices have to. It's more difficult to get a driver's license, than to find a job for an illegal.
Your wife speaks English. Most illegals can barely speak English. It doesn't take an Einstein to look at a bunch of people and be able to tell if they are illegals.
Racial profiling is already done on Arabs. If you want to be PC, you may as well give up and take it from behind from the government, in the fear of offending some group. The government knows one thing, and that is to ensure the smooth functioning of the society, and whether this happens after America becomes a police state, is a lesser concern to them, than losing that fight.
Without a job, whatcha they gonna do? Add some harassment from the authorities, and they'll crawl back across the border.