Well, what is wrong with any variety of line-jumping? It takes a spot away from somebody willing to follow the rules and wait his turn to become a legal immigrant.
I can accept this as a legitimate problem, but that's only because I don't know what the rules are and how long a person must wait his turn. Desperation plays a huge part in what rules people are willing to break, and in those cases (which may be a few or a lot, I honestly don't know) I disagree that "The fact that he chose to line-jump and risk the wrath of the government instead of waiting his turn and going through the legal procedure is a red flag that he's probably not actually any time soon going to become productive enough to make taking him in worth the consequent costs to the locals." You prefaced that with "provided there's a rational immigration policy, the government would have given him permission." Do we have such a policy? Depends on who you ask, as this thread demonstrates.
Note that most people have no way to even get in line.
- - - Updated - - -
The last time the U.S. had open borders it resulted in a massive boom that made her the most powerful nation in the world.
Clearly it would be disastrous to let that happen again.
When we had open borders we weren't much ahead of the rest of the world. It was a land of opportunity, not a land where you got an automatic major step up in coming here.