I think the job analysis is overly simplistic. The reality is that worker migration from poorer countries to richer ones is a huge low wage problem. Instead of allowing low-skilled labor to pay better in order to attract workers who expect better conditions, you keep the wages fixed and import workers for whom even the bad life you're offering is better than their current life.

Of course, this doesn't mean that allowing 0 immigration in is the right solution, or preventing immigrants from working. And I should also point out that, generally, US leaders have the least amount of problem with this aspect of immigration - even now, Trump has instructed ICE not to go for deporting agricultural and tourism workers in any mass numbers.