Your heavily restricted, highly educated, legal immigration examples are a tiny fraction of what immigration is in the US. The tens of millions of unskilled illegals allowed into the country is a wage suppression tool.

The peak of immigration was 2.4 million, maybe the tens of millions of non existent people would certainly affect wages.

But maybe decades of anti unionisation efforts, manufacturing displacement and lack of updates to minimimum wage, healthcare provisions and general safety net have a higher impact on keeping wages low. Idk, the possibility of dying without access to a doctor if you dont work might keep people from asking for a higher salary if you think about it for even a fraction of a second.

Also there are 1 million concurrent international students while on average the USA receives around 1.5 million immigrants per year. which means that there are a 60/40 split. With many students returning to their countries but similarly many legal immigrants having temporal visas like H1B and conditional stays (marital, family visa, contract visa or refugee visas).

The percentage of immigrants is also been stable since the 1870s around 12-15%. There was a depression during WW2 with it going as low as 7% in the early 50s, which has little to do with immigration and more to do with millions of deaths globally. Also it rebounded to 13% quite quickly and has been there since the 60s with no meaningful relationship between wages and immigration numbers

> Your heavily restricted, highly educated, legal immigration

The two countries with the highest immigration to the USA behind Mexico (which is obvious due to proximity and opportunity), are India and China.

The best mathematician in america is an immigrant in Terrence Tao. The biggest tech companies are headed by immigrants or sons of immigrants (satya nadella, elon musk, jobs, Lisa Su).

Like you can argue that the GDP going up is responsibility of immigrants as much as you can argue that there is wage suppression due to immigration