Since immigrants are much poorer on average, they spend less than the native population, and often cost more in welfare etc. So the costs of immigration are borne by taxpayers and native low wage workers, while large corporations and business owners reap the benefits.

Yes.

But, lowering tariffs also lets cheap chinese assembly line shoes be shipped to the US for 80 cents less than what it costs to manufacture on shore.

The 80 cents saved does not matter to the shoemaker who lived to sell shoes all his life, has 2 kids and a mortgage, and suffers early retirement due to unfetted globalization.

Immigrants can only increase demand that is less than the value of their wages. There is diminishing returns in adding more people to a situation.