If your goal is to reduce illegal immigration, a much cheaper way is to heavily fine anyone who employs someone without a valid work permit. For most illegal immigrants the motivation is economic and this would reduce that motivation and bring in money from the fines instead of incurring massive cost from detention and deportation without the negative side effect (?) of deterring tourists and legal immigrants.
(Of course, I think the entire goal is economic foot shooting)
The UK does fine employers, its not sufficient to stop it because people work through dodgy contractors.
The UK also fines landlords which has caused problems for people who look or sound foreign, including some British citizens (especially poor ones who tend not to have passports which are the easiest documents to check).
The best proposal I have heard is to provide a cash reward to illegal immigrants for turning in people who knowingly employ them illegally.
The fact that governments do not try these solutions makes me suspect they want to keep that supply of cheap labour - most illegals here work for well under minimum wage.
Yeah, it's totally doable for the US to deport all the illegal immigrants. The consequences would most likely be pretty high inflation, but it's totally doable.
While I dislike the UK requirement to have a passport on your first day at work, I understand why it exists.
The dodgy contractors take a markup for taking the risk away from employers. A lot of them are criminals with connections to people smugglers, are both willing and able to get away with things someone with a more legitimate business would not. They are a layer of plausible deniability.
(Of course, I think the entire goal is economic foot shooting)