About a full THIRD of immigrants to America from Europe during 1900-14, before the Immigration and Naturalization Act of 1917 (complete with Asiatic Barred Zone), ended up back in Europe
The Business of Transatlantic Migration between Europe and the United States, Keeling, p.201

The reason America had so much *historical* immigration success is two-fold:
1. It didn't give them anything like the immensely generous welfare, public services, and almost preferential treatment in labor and housing markets they get today, even illegals
2. It send a lot back

The story of America's immigration laws from the 1790 Immigration Act up until 1965 is one of increasing restrictions.
The US expanded its territory and opportunity, while raising the bar for anyone to come: *DUH* of course that would work.
It became better/exclusive in tandem.

Notice how that's basically the exact opposite of what US immigration law and policy has been since 1965, which is summed up as "Everyone can be an American! We're all Americans and America is for everyone!"
A public bathroom country, a bus stop country, a motel country.