The labor market is something that emerges from the equilibrium of several opposing forces. We as a society decide which causal factors are 'reasonable' and which are 'unfair'.
As a simple example, you could argue that 'the wages for married individuals with kids are depressed due to the massive labor pool of single people in their 20s who can be employed for far less as long as you offer them free food and some cutesy perks like happy hours and pool tables'. Ceteris paribus, and as a pure fact of economics, this is true. Of course if you have a bigger supply of labor and hold other things constant, wages will depress, but as a matter of practical policy, we don't consider it 'unfair' that there exist single people who are competing for jobs that married people are also competing for.
But many people do consider it unfair that there exist Indians who are competing for jobs that Americans are also competing for.
This is a matter of policy and your personal sense of what is fair and what is not, not economics.
Single people tend to be younger and less experienced. They tend to be represented in entry level positions, and get paid as such.
That appears to be the reality we've been living in for a couple/few decades. Airplanes, container ships, and the internet have made the world a much smaller place.
So, immigration is generally speaking something that corporations are incentivized to want because they get more manipulatible and desperate employees?
Can we just demand that companies that hire immigrants cannot fire or lay off those immigrant employees for some minimum number of years unless they declare bankruptcy? It might decrease the number of immigrant employees corporations would hire but it would simultaneoulsy ensure a huge amount of safety for the immigrants that do get hired (and for their families).
As long as the "risk of having to leave the country" for speaking up about anything is greater than 0% the obviously-wisest thing to do is keep your mouth shut.