#13 They're illegal.
#12 No centralized government for most of its history? I'll let that one slide as a typo.
The difference between today and the periods of great migration is that we are now a welfare state.
Milton Friedman was spot on when he addressed immigration in the welfare state:
Immigration is a particularly difficult subject. There is no doubt that free and open immigration is the right policy in a libertarian state, but in a welfare state it is a different story: the supply of immigrants will become infinite.
In the above quote, he is actually referring to LEGAL immigration, whereby legal immigrants have access to social programs and therefore become a burden on the budget. He further addressed ILLEGAL immigration:
Look, for example, at the obvious, immediate, practical example of illegal Mexican immigration. Now, that Mexican immigration, over the border, is a good thing. It's a good thing for the illegal immigrants. It's a good thing for the United States. It's a good thing for the citizens of the country. But, it's only good so long as it's illegal.
You see, as soon as we legitimize the immigrants that have crossed the border illegally, they become eligible for social benefits. If they remain illegal, they don't. What Friedman failed to count in his comment was the "anchor baby", of course.