There aren't all that many immigrant nations like the US though. Canada, Australia, New Zealand, that's pretty much it? Maybe Singapore or the UK at a stretch.
I agree there aren't many. It still is myopic to view this as something specific to America, as opposed to a generic quality possessed by all immigrant-dominated societies, and the fact that there are only a few such societies doesn't change that. Many (obviously not all) American authors do tend to view it in that myopic US-centric way. America is never as exceptional as some Americans think.
Most of the Caribbean (save Cuba/DR?), Taiwan, Mauritius, Seychelles, Maldives, Argentina, Chile, maybe Uruguay/Costa Rica/Panama. Singapore doesn't seem like a stretch. The UK doesn't really count. Granted, most of these are pretty small.