An interest rate change tomorrow will have an immediate impact and shift longer patterns but can be undone or furthered at a later time.. and 10 years from now, it will be lost in the noise.
They want a bigger pie because then their companies have bigger markets to sell their goods. If it comes at the cost of increasing the population so that everyone else is individually poorer, they don't care. You can't become a billionaire in a country of only 100,000 people. There aren't enough people from whom wealth can be concentrated.
You can envision a scenario where this doesn't happen because the new workers earn so little that the new demand they create is tiny, and their employers don't spend their savings on things that ultimately create more employment. (Like if 100 people showed up and started doing work for $0.01 apiece that the previous employees did for $1,000 apiece, and the employer decided to spend the whole $99,999 savings on some good that has very little labor input and that somehow also fails to have a significant multiplier effect that generates employment. In that case, while there has been an increase in total economic activity, there hasn't actually been an increase in employment.)
This latter scenario seems pretty unrealistic to me, but I don't know exactly how to describe the conditions under which it would or wouldn't occur.
There are plenty of ways corporate executives can spend their labor cost savings that do not produce nearly as much labor demand for Americans as was lost to immigrants. Most notably, they can take their assets overseas where no American worker will see a penny of it.
That's exactly what nations do for legal immigration.
But for illegal immigration there's no knob.
(Well, no pleasant and easily controllable knob).