It worked back then because before the 1920s, the US simply did not control its borders. The only immigration restriction was the Chinese Exclusion Act, a special case. 1/
During the 1910s and 1920s, a nativist backlash — arguably to precisely these effects though of course nativism always takes on ugly racial/cultural overtones — basically froze immigration at a very low level. 2/
That wasn’t undone until 1965, which gave us our current immigration regime. Restrictionists want to go back to the mid-20th-Century regime, detest the Immigration and Nationality Act of 1965. 3/
The history you extol just happened before we invented the tools, developed the capacity, to make management of immigration a subject of policy. We’re unlikely to uninvent those tools. We are living now through a period analogous to the 1910s/1920s backlash. /fin