I haven't read his book. But Borjas, who is to be clear a bit of an outlier among economists who have studied the problem, has in the papers I've looked at estimated that immigration is (slightly) a net economic negative for the very least skilled workers in the first world. This is nowhere close to saying that the net economic effect of immigration, including the benefits to the immigrants, is negative.
It's a short and well written book, I'd recommend it if you're interested. One point that Borjas makes repeatedly is that he believes there is a suppression of reporting on the negative impacts of immigration liberalization. He also notes how on several occasions colleagues expressed surprise and dismay that he chose to publish findings that "went against the narrative", out of fear that they could embholden enemies of liberalized migration. Therefore, I would be cautious of drawing much from consensus or deviation therefrom.
> has in the papers I've looked at estimated that immigration is (slightly) a net economic negative for the very least skilled workers in the first world.
How can you possibly recognize this and still decide that your proposal makes sense, in light of events like the presidency of Donald Trump and Brexit? What we have now is a drop in the bucket compared to unrestricted migration, and it's already quite possibly indirectly causing massive political upheaval that threatens to destabilize the first world.