The US were fairly unique for being a very open, free and prosperous society, which happened to also have vast unsettled territories and an insatiable hunger for immigrants. Even if the US lost a couple of wars, got humiliated by the Brits and never expanded west, there would still be enough wide open space in Kansas, Dakota etc and hell even in Pennsylvania, Ohio, and Michigan for millions and millions of immigrants.
People didn't move to the US because they liked living in a dominant country, on the contrary many left dominant countries like Britain Germany or Russia because they wanted to live in a free country where they would be left alone by the state and could have a better life than back home. Unless the USA are carved up by Russia and Mexico or become an oppressive dictatorship, I don't see why that should change. The USA could remain happily isolationist and they would still be the most attractive place in the world for immigrants.
[...]
I think a nice way to model the push and pull factors behind immigration would be to assign province RGOs with a max RGO capacity (dependent on technology, local prosperity i.e. local POP wealth etc), and have the gap between max RGO space and actually filled RGO space be the driving force for immigration. People would go where there is "free space" for them, i.e. a place where they can make a good living with the least effort.
A desert province would only have a very low max pop, but as the province is economically developed the max pop increases. Climate and suitability for agriculture would be obvious factors that go into max RGO size. But also mineral wealth and accessibility (=infrastructure) of a province. For example in 1848 Nebraska might be a howling wilderness, with a handful of Indians who possess nothing but a handful or horses and their teepees, a low-value RGO and no infrastructure to speak of. An unattractive place, in other words. But as you build roads into the province, the RGO capacity increases, also when Nebraska changes from an low value RGO (cattle) to a better valued RGO (minerals? fruit?). Immigrants start flocking into the province. The immigrants become farmers, the "GDP" of the province increases. Now the rate at which immigrants move in to fill the RGO gap increases, and the trickle accelerates. The gap fills faster. Eventually though, unless the province changes to another yet more attractive RGO or tech changes the max RGO size, the province is "full", and new immigrants will move to some other place. The local POPs' natural growth will still lead to growing population but the immigrant flood heads somewhere else.
[...]
Having the RGO gap as a driver for immigration would be useful to model why exactly people wanted so badly to go to the US, and not other equally underpopulated countries. They wanted to make a living on their own land. In the USA (or any free country) the strength of attraction of an open RGO would be stronger than in an unfree country. Also since potential RGO size is dependent on technology, underdeveloped countries see less immigration. Lastly taking into account the "local GDP" as a factor in the attractiveness of a province would make it so that immigration will not just head into the first best prairie province, but instead people will seek out the low populated land at the edge of the settled frontier, rather than head straight into the howling wilderness. This could even cause immigration to move like a wave, saturating the frontier provinces before moving on to claim totally new untamed lands in the Indian Country. It would also make a prosperous country of opportunity more attractive than a less prosperous country of opportunity, all other things being equal. Africa may have as much open spaces as America, but people prefer to go to places where they don't have to wipe their ass with sand, so to speak...