Chiswick is not saying that immigration is good for us. He only says that at the beginning of the article as a way of setting up the opponents' argument so that he can knock it down.
What Chiswick is saying is that there are plenty of Americans who already do the "dirty jobs." He is saying that if there were fewer low-skilled immigrants there would be no choice but to have Americans do those jobs. Wages for those American workers would go up because there would be fewer workers to drive wages down.
Chiswick is also saying that there would be other impacts. Prices for some things we buy would go up because the workers would be making more money. But those workers would have more money and would be able to buy things and help the economy grow.
Overall, then, Chiswick is saying that fewer low-skilled immigrants would force employers to hire American workers and that the lack of competition would drive wages up.