Looking at the US Census data from 1850 onward (they didn't ask where you were born before the 1850 census), the percentage of the US population was a steady 13-14% from 1860 to 1920. In 1950 (they didn't ask in 1930 or 1940), it's down to 9% presumably from the changes in immigration law in the 1920s. Then it's around 5% for 1960-1980 and from 1990 starts to rise up to 12.48% today. That's roughly where the percentage of immigrants was for the 6 decades before 1920. That doesn't to me look like "an unprecedented experiment with extraordinarily high immigration"
Despite reaching replacement level fertility in the 70s, the population has continued to explode, and this is due entirely to immigration. This is historically unprecedented.
