Once again, here is where you are wrong.
Legal Aliens (Non U.S. Citizens) are not here working out of their own pocket. Most of the time they work for somebody who pays their work visa (H1B, T1, etc.) and helps them find jobs.
Now, If I am paying this "foreigner" $50 per hour, the company who is paying his visa gets 20-75% of what he makes leaving $12.5-$40 per hour for the person actually working.
So tell me... all of those tax breaks that I assume you are talking about... does that really add up? Do you still think that their cost of living is lower?
However, if you are talking about foreigners outside of the country, if you read carefully, my example was not using someone outside the country.
99% of the time its not individuals who are contracting from outside of the US, its companies.