For a lot of immigrant Germans leaving Germany is very much a goal, since upward mobility in German society is very low compared to the US. So for a lot of "German Germans" the answer is no, but for the rest it very much is something people aspire to.
If you look at the statistics I believe outward migration is a little under inward migration, but I'd wager that there are a lot more people with higher ed moving out than are moving in.
I complain about the US a lot, but for me both the US and the UK were vastly better for my mental health and career than Germany was, even despite the average standard of living in Europe being much higher.