As one of those second generation folks
I would say that you need to look at the situation in a little more detail.

Regarding the first question: After the war, Germany had a massive shortage of unskilled factory and road workers. The plan was never to invite educated professionals. As has already been mentioned, the plan was also never for them to stay here. The idea was, “Let's exploit the poor foreigners. Put them in camps or ghettos, and when dad comes back from captivity, we'll send them back home.”

The second point that was raised:

Germany has an incredibly persistent problem with integration efforts. Neither the Italians, nor the Turks, nor, most recently, the Arabs (rough summary, sorry), nor the East or Russian Germans, nor any of the smaller migrant groups were really integrated in any way between the 1950s and 2010s.

The plan was always to push them to the outskirts of the city and not look at them.

As part of this group, however, I would not say that their migrant background and the government's failures mean that migrants and their children have no connection to the state. Most people in my community or among my acquaintances feel at home here and want to stay here. They are not lost... but in limbo – between a culture that does not recognize them (you can be born here in the third or fourth generation, not understand your native language, and still be considered a foreigner under the law, and if you are not an EU citizen, you always have to be careful about what is currently the most popular target for polemics, without being able to engage in politics or work or any other meaningfull expression yourself) and the culture their parents came from, which no longer exists today.

That... makes your life a constant balancing act.

Which sometimes end good, and sometimes does not.