Yes, I'm saying that it doesn't accomplish the stated goal. Restrictive immigration policy is worse than a more welcoming policy when you consider the impact on all existing Americans. Immigration is the better policy for Americans, it's just that the benefit is spread out across more people than the downside, so it is easy to think otherwise.
As far as retraining and such, we should seek to design such things so that they are highly available and are beneficial to the United States as a whole regardless of whether you train an immigrant or a first, second, third, or fourth (or fifth or sixth or seventh) generation American.
W/re training. America is responsible for training our own, I don't think we should think we should off load that job to say Canada, and in the same way people's home countries should be responsible for their own citizens wellbeing and development. We cannot be responsible for nor absorb the deficiencies by other countries with respect to their own citizens, in effect subsidizing malgovernance.
So yes, you are wrong, both about the impact of immigration here and the impact of closed borders elsewhere.
With the training I see it as a utilitarian issue. If training someone is a net benefit to the US I don't care where they were born. I certainly don't want to leave the benefit sitting on the table just because they weren't born here.
But often not per worker-hour.
[1] https://loc.gov/law/help/points-based-immigration/index.php
But with re Americans over other Americans, yes, it makes sense to handicap underprivileged Americans. Give them a leg up on education, training, tax breaks, etc. before we even begin to think of how we can benefit foreigners.