It's easier than that, I am not a pro, and even I can tell when I am near an illegal. They carry themselves differently than an American latino.
Profiling works and is good. You check ID and if they have a legit one, that is it.
If illegal, show them the door.
Ah, so in other words, we should have Gestapo agents stopping people and asking for their papers at every turn, at least those with brown skin. Uh-huh.