H-1B, the input stream for these skilled immigrants, do not have any such per-country limits. But the green card process does. This brings into existence a large number of skilled immigrants who have their stay in the country tied to their job. This weakens their negotiation power, and contributes significantly to the wage depression you talk about.
Even NumbersUSA do not oppose removing this [1] restriction. Yet, you are _for_ keeping the per-country quotas. Why?
[1]:https://www.numbersusa.org/content/news/november-30-2011/sen...