The truth is, assimilation is usually a process that takes a generation or two. First generation immigrants don't assimilate very well. Many never manage to even learn the host country's language.
Assimilation really happens at the level of their descendants, who grow up entirely within the host country, going to their schools, consuming their pop culture, etc, and think of themselves as Swedes or Americans or whatever.
It takes a lot longer if the immigrant groups are (locally) large. They are a lot more than just locally large in Sweden. It also takes a lot longer if the state bends over backwards to accommodate the immigrants, which Sweden does.
Assimilation really happens at the level of their descendants, who grow up entirely within the host country, going to their schools, consuming their pop culture, etc, and think of themselves as Swedes or Americans or whatever.