This ought to be true in theory. It does not work so well in practice.
In practice we are not getting very much high-skill immigration. What we are getting is a subservient and mostly docile immigrant workforce that is used to disempower the natives. That is the entire point of it.
Rulers have been playing this game at least since Babylonian times. It generally works well for them, for as long as they live. In the long run, the immigrants become the new rulers.
As for the natives - they usually don't do so well.
We don’t get much high skill immigration because we make it very difficult for such people to come and stay, whereas we allow in many legal and illegal low-skill immigrants whose offspring at least three generations in continue to be low-skill drains on us.
Countries like Canada and Australia have figured out how to allow in the high-skill folks only—and they do help those economies quite a bit. As I posted elsewhere on this thread I’d be fine with stopping immigration altogether for a period of assimilation, but yes, even high-skill people if allowed in should be allowed only in moderation.