The lines are not arbitrary in any meaningful sense. Leaving aside that the lines are typically drawn by blood and treasure, they have a very clear meaning in terms of how the government relates to the people in different places. Given that government is largely self determined by the people, would people who were able to establish a relatively benign government want people who were unable to do so in their own lands to be allowed in? Do people have no interest in determining to some extent the makeup of the group determining the nature of their own government and society? I think they do. America is not just or even primarily an area of land, it's a set of ideals, cultural, and governmental practices that is wholly dependent for its existence on its people maintaining those traditions. You couldn't just throw a random assortment of people into America and have it still be America. You need people who either are American and have been raised and school in its cultural traditions and mores, or you need people who seek those values for their own sake rather than because they're fleeing somewhere else. Allowing people in who want to be American is fine, allowing people in who want to be Mexican or Salvadoran or Chinese or whatever but take advantage of American culture and governance without personally investing in the ideals that make that system possible are not. It's silly to think we could allow in an unlimited number of people who don't understand or value the American way and not see a significant degeneration of our culture and governance.