I've never heard it either. Immigrants migrate overwhelmingly to escape terrible economic circumstances, wars, or simply to escape whatever oppression or danger is making their lives much worse than they could be.
However, you must remember the bit about limiting who is allowed in the country. If you were a German with a hypothetical burning desire to flip burgers at In-N-Out Burger, what are the chances of you getting a work visa? I would say effectively nil. So you're not going to see those people even if they would arrive in a world without borders.
> If you were a German with a hypothetical burning desire to flip burgers at In-N-Out Burger, what are the chances of you getting a work visa? I would say effectively nil. So you're not going to see those people even if they would arrive in a world without borders.
That's a great point. Legal immigration (to somewhere desireable) is not an option for much of the population. What interest do they have in preserving it?