Different conceptions of nationhood have different implications for immigration. If the American experience is reducible to American political ideals, then the only assimilation that should concern us is to those ideals: As long as new immigrants are no threat to freedom of speech and the rest, all is well.
If a common culture is important too, though, we will want immigrants to assimilate to it, even as they also change it. We will want natives and newcomers alike to see themselves as belonging, together, to it. And we might decide that we want a smaller influx of immigrants in order to encourage that kind of assimilation.