First, the practical case: when I was in college (2000-2003), none of the Indian or Chinese people wanted to get a job back home. And, they were some of the best people in school: the more advanced the class, the smaller the proportion of native born Americans; graduate level classes were mostly full of foreign-born students, and most of the top of the class consisted of foreign-born students. The U.S. didn't let most of them stay in the country, forcing them to go back home. If you take a bunch of smart people, and force them to live in their home country, they aren't going to go dig ditches; they're going to start industries. Those industries have done so well that many of my classmates (and others) who have spent time working in the U.S., and have a legal right to work here, want to go back home. They, naturally, want to be near their families. A decade ago, there wasn't enough industry to find a job that was both interesting and well paid. By forcing the people who wanted to stay here to go back home, we've forced them to create good companies, and hence, good jobs.
And then there's the moral case. This is less relevant for high-skilled workers now, due to what's happened above, but it still applies for many countries and most industries [1]. If we reduce the wages of engineers in the U.S., we're reducing the wages of a relatively well off group in one of the richest countries in the world. We're talking about reducing the wages of someone who is, on a worldwide scale, in the 99th percentile. If we let someone in from a poor country, we're increasing the income of someone who might be below the 50th percentile into the 99th percentile. It's awfully hard to make a case that we should be enriching the richest people in the world at the cost of the poorest.
[1] Total factor productivity [2] in the U.S. is so high that unskilled Mexican laborers become three times more productive when they cross the border, and, globally, Mexico is one of the richer countries in the world.