Yes, yes--Hell Yeah, you have it explained perfectly The money goes out of our "economy" and in to theirs. But it's just the money. It has another component. The WORK. The work stays here. It has already been done. We get the work, they get the "money".
You think that is a bad thing? Seriously? OK, then look at it in another way. We get the PRODUCTIVITY, they get the increase in money supply.
I mean you understand that the Federal Reserve just cranking out the dollars is not a good thing, right? More dollars, same amount of goods, or works, or resources. Whatever, it don't make a shit. Well then why can't you understand the taking out dollars, "poof", disappearing them in to some far off foreign land, while at the same time creating more "work", or goods, or resources here is an awesome thing.
Damn, like Japan printing a boatload of counterfeit money and dropping it in the US economy. Damn near the same thing as the money immigrants "bomb" the countries where their families are. It was considered an act of war back then, now you act like those receiving countries are winning the lottery.
Now, here is how that whole immigrant workers increasing pay works. Let's say you are a bricklayer. Your employer hires an immigrant worker to haul the bricks and make the cement. You used to haul the bricks and make the cement. He makes less than you. Now you have more time to lay bricks. Your employer get's paid by the brick. Now he can pay you more, pay the immigrant, and still profit from the increased, wait for it, PRODUCTIVITY. You did get that, "profit more", right?
No matter how you try to spin it. No matter how much your bias draws you to the conclusion that immigrants cost the US, you are wrong. It is hard to find an economist that would support your position. And history doesn't support it either. When immigration increases productivity, and wages, increase along with that increase. It has been proven time and time again. And perhaps more importantly, when we restrict immigration too aggressively, our economy tanks as productivity declines and creativity and ingenuity drop.