> Those countries were not keeping for high skilled immigrants.
The US, UK, and Canada all have special provisions in their immigration programs aimed at attracting and prioritizing highly-skilled workers.
Both the UK [1] and Canada [2] both use a points-based ranking system that prioritizes highly-skilled immigrants. The UK system is clear in its goals:
> introduce an Immigration Bill to bring in a firm and fair points-based system that will attract the high-skilled workers we need to contribute to our economy, our communities and our public services.
And while the US H1-B program is lottery-based, 20,000 slots are reserved for people who hold a master's degree from a U.S. institution. Proposals have also been made recently to change to a points-based system. [3]
> They built themselves into places that high skill immigrants seek, but that is more of a side effect than a competition
Wherever there is choice, there is competition. 55% of billion dollar startups in the US have immigrant founders, employing an average of 1,200 employees each [4]. If these people don't come to the US and start companies, the US will feel the effects - even if they were just "side effects".
[1] https://www.gov.uk/government/publications/the-uks-points-ba...
[2] https://www.canada.ca/en/immigration-refugees-citizenship/se...
[3] https://en.wikipedia.org/wiki/RAISE_Act
[4] https://www.fosterglobal.com/blog/55-of-americas-billion-dol...