The humanitarian argument would compel us to bring the entire third world population here.
Imagine you are in London on a visa that expires next week, and there is a highly contageous disease spreading through the US. Would it not be the right thing to do to allow you to remain? In fact, would it not be insane to force you to go back?
The same argument would hold that we don’t deport any illegals that are obviously already here because there is disease and war etc. in their countries of origin.