That's a pithy description of it all. If I hadn't met my (Greek) wife in 2015, I've probably would have left long ago.
And to come of think of it, I think there is another aspect that influences this: Germans are not having as many kids as the immigrants, so the overwhelming majority of the kids in the kitas and schools are from immigrant families or immigrant/native mixed parents. This means that (at this stage in life) any new friends you get to make are likely through your kids, and even there the pool is selected against Germans.
That's a very Berlin-centric observation. Berlin is special; it's hard to extrapolate to the rest of the country.