I think you’re taking my comment rather more personally than is reasonable. I don’t have any idea what you believe, who you sympathize with, etc.
You said “Cohesion of the whole can be impaired despite all the parts being of good quality, if they do not fit together very well.”
This sort of vague analogy has been a common rhetorical device used by anti-immigrant populists trying to stir up nativist resentment for 150+ years, without any strong evidence that it’s true. I’m calling the specific sentence out for being usually, in my opinion, toxic nonsense.
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To answer your previous points:
As for the effect of immigration on labor markets during the Gilded Age, I’m not enough of an expert to say. That sounds like a topic which could fill a few academic research careers in labor history and produce several books (or probably has).
On the other hand, the research I’ve seen about low-skill immigration from Latin America in the past few decades has seemed reasonably convincing that such immigration has not had dramatic downward effects on wages for native workers and on average has boosted local wages by strengthening the economy generally, and that downward pressure on wages for unskilled factory work, etc., has a lot more to do with other factors (changes to labor law, global trade, automation, etc.). There’s obviously a lot of debate and controversy about the precise details.
> Germany, Ireland, Italy, Poland, etc weren't drastically more corrupt than the United States a hundred years ago, were they?
Well, they were all feudal societies with a landed aristocracy ruling by force of arms, with most of the migrants being rural peasant farmers driven off the land (often forcibly) and forced to migrate abroad due to population growth and lack of local employment opportunities. I’m not sure what you count as “corrupt”. In my opinion everything about a feudal society is inherently corrupt.
The situation of peasant farmers fleeing these countries is actually remarkably similar to the situation of migrants from southern Mexico in the 1980s–2000s. If you took my Irish ancestor’s story from the mid-19th century and set it side by side with the story of a rural Mexican peasant migrant from 1995, and changed all the names in both stories, you wouldn’t be able to tell which one was which.