This contains a common logical error in most of the poor-people-suffer-to-serve-us-rich-people arguments. That is to ignore anyone whose suffering has no causal link from us. For example, an isolated tribesman may die from an easily treatable disease because he has no medicine and we don't blame rich people for that. But if he moves to town to earn money for medicine and then dies in a construction site accident, we blame ourselves for causing the construction site to exist. We forget that he may have been in greater danger or suffering more before getting involved with us.

It applies to low wages for illegal immigrants too. Once they're in our country, we feel responsible for them. Before they got here, we don't care at all how little they earn. Some people even go so far as to want to kick them out to save them from earning low wages. Really it just saves us the guilt but makes it worse for the individual.