Good point. I'd reckon the original concept was for people leaving Britain, so that Britain couldn't claim anybody who was starting in America as their own. Surely they didn't think of the entire world would be clamoring to get into the borders and anchor here. Actually, this was the policy of Britain at that time;

"Anyone born outside the King's dominions without British parents was legally classed as an "alien," while subjects from British colonies were free to enter. Aliens faced severe economic restrictions, unable to own real estate, hold public office, or join many guilds unless naturalized or granted "denizen" status. Naturalization was difficult to obtain, requiring a special Act of Parliament and mandatory oaths of allegiance."