Effect of immigrants on relative wages are very modest. Effect of high skilled immigrants on productivity are massive. From a welfare of natives view, u would focus on more high skilled immigrants as the #1 priority. Less low skilled is extremely minor issue.
Those who feign a hard headed economic and native welfare only view of things suspiciously prioritize decreasing low skilled.
Here, for example, is a good quote from Gordon Hanson: 
The obsession with negative effects of low-skilled immigration, which is probably zero and at worst an extremely minor factor, is a tell. Take George Borjas who straight up says he isn't interested in innovation, productivity, economic growth effects
Low-skilled immigration is under nobody's estimates an important driver of outcomes for the low skilled natives. Productivity growth, economic growth, innovation, dynamism, and entrepreneurship matter A LOT.
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