Your view of current immigrants is not that different from the Germans in the 70s who thought that the Turks and Vietnamese looking for jobs in Germany would go back to their homes after a while. Some of them did, but enough of them stayed to become a substantial part of the population.

Anyway, like I said there is a good chance I am wrong about it Germany in general. But I'd argue that in Berlin that is pretty much the case, regardless of how large the "transient" people are compared to "longer-term settlers". Once people start having kids they stop hopping around, so I'd guess that the amount of "non-native" children that dominate the schools have immigrant parents who are mostly settled.