When it's easier, cheaper, and less dangerous than coming across the border illegally? Yes, I do. These people don't particularly want to be illegal, they want to be in the US.
Hundreds of millions of people around the world also want to come to the United States. That's why we have immigration laws and quotas, to make immigration an orderly and measured process. If we implemented your idea, we might as well get rid of our current immigration laws because foreigners around the world wouldn't even waste their time filling out the necessary paperwork to come here. They would simply hop on the next plane to the US, and after arriving, they would say that they're planning on staying and want to become a US citizen.