"hardly an economic practice which needs to be perpetuated"
So you would rather send your money to some South American country, than allow migrant workers who will work for the wage into this country. Have I fairly stated your position?
If an economic practice is valuable, the marketplace will recognize that value. On the other hand, if an economic activity exists only by virtue of subsidized labor, the free market would not long tolerate it.
Yes, I'd rather pay a farm worker to harvest in South America than in this country.
That way, I don't have to pay his emergency room bills when he gets sick, pay for his kids' education, pay for his kids' medicate, or pay for any of the countless other government services illegal aliens use.