Between 1921 and 1965, about 9.6 million people were admitted as lawful permanent residents. That's not what I'd call a "very small" or "highly restricted" inflow.
We have been around 1 million per year for decades. If we still had that policy, adjusted for population you’re talking about cutting legal immigration by one-third to one-half.
And that’s not counting a large increase in “gray market” legal immigration (TPS, asylum, etc.)
Source: DHS Yearbook, https://ohss.dhs.gov/topics/immigration/yearbook/2019/table1...