Our immigration system is our biggest advantage? Are you sure it's not the thing(s) that makes people want to immigrate here that is our biggest advantage?
Getting one started usually isn't a conscious policy choice. You have relatively better conditions to start with (no war, good location with stable climate, good civic institutions, limited immigration restrictions) which kicks off the virtuous cycle.
Here's an example. The Irish famine led to Irish emigration down the road, which benefited the US and Australia. This wasn't a policy choice of the receiving countries. It was mostly luck. These kind of relative differences in liveability between the two countries (US > Ireland) leads to a positive feedback loop in the US.