If being undocumented is a crime, people accused of it are entitled to trial by a jury of their peers.

FWIW, that's not strictly true. We deport non-criminal foreigners for diplomatic reasons all the time. I think it's very reasonable to imagine an enforcement regime (not the one we have) where legitimate workers (and their families, yada yada) have easily-available and auditable visa and citizenship documentation. And so if you find someone who doesn't, there's no failure of due process to simply deport them. Done right, there won't be many cheaters anyway as employers will have easy access to documented labor instead.