I think you're getting it all wrong. There are two different things to this. Corporations wants to pay lower wages. No doubt. But also they want skilled workers. If the skilled workers want higher pay, are you saying they won't pay? Of course they would. But if you can get that skilled worker and still pay lower wages, that's a bonus for them. Even you in their shoes will do same. It's just the economy and market conditions playing side by side. No judgement. So this your statement: immigrants are entering the west because some corporation wants to pay lower wages is all switched. What about those that just want a better life? Are you saying they want lower wages? You're classifying only a few to equate everybody. That's not right.
You have said a lot of things I have in mind already, but their are few things I wish to add to what you have already said. As a business person, you will always care more of the interest of your business, because if the indigene don't have the required skills needed to carry out a job, or they have it but what they are demanding as pay is unrealistic, you will want to go for a cheaper alternative, because the most important thing is getting the job done.
Another thing is that these immigrants that comes to work are mostly the ones keeping the economy running because majority of them are skill works, because if they decide to go back to their various nations, it would be very difficult to replace them with the same cost.
Example, a plumber in America that is from Asia may accept to do a particular plumbing job at a lower cost because in his country, that's a lot of money, but for an American plumber, he wouldn't want to accept it because he will feels like it's too small for him, so it's wrong to put all the blame on this corporation because they are doing what is necessary to keep the countries economy afloat, which is also of interest to them.