Of the advanced economies, Western Europe seems to have the exact issue identified by GP: the hardest working/most ambitious workers move to the US. On the other hand, in Japan "death by overwork" seems to be close to or at the level of a genuine public health crisis: https://en.wikipedia.org/wiki/Kar%C5%8Dshi
This isn't obvious at all. A few very specific, niche employment areas in which the US dominates (software engineering in certain niches, medical practice, and maybe show business) have a modest influx of Western European workers, but that says nothing.
Among the reasons for emigration to the US, there's not a single living soul that says "oh, I'm not legally allowed to work enough in my area of employment to achieve my dreams". It's a laughable and ridiculous statement.
If the US implemented more reasonable restrictions on labor in the US do you propose the hardest working most ambitious are going to move to China or Brazil?
Of the advanced economies, Western Europe seems to have the exact issue identified by GP: the hardest working/most ambitious workers move to the US. On the other hand, in Japan "death by overwork" seems to be close to or at the level of a genuine public health crisis: https://en.wikipedia.org/wiki/Kar%C5%8Dshi