I am speaking as a non-German native English-speaker who lived in west Germany and am now in east Germany.
I cannot say for sure that integration has failed. I can only self-report what we have seen on the last decade since living here.
Firstly, the education system is fantastic. We have really no complaints. The Germans are strict but very, very thorough and encourage dedicated students from the first grade. Our two are learning their 3rd language in the 6th grade, as well as physics, had biology in the 5th, and then do latin and chemistry in the 7th. Really have nothing to complain about. However, the rest of the integration stuff has me worried.
Certainly, as you would expect in all big cities, Berlin and Munich seem very multicultural and therefore very tolerant. So many languages are spoken and no-one turns when they hear Arabic, Spanish or English in the supermarket, for example. However, DH and I have observed people being openly racist so many times, and there is a strong anti-Muslim sentiment, especially in the last few years. People I would expect to know better, as in, people in higher public positions and those who have been well-educated are often the most vocal.
In the east, there is even far less tolerance. The AFD, a far-right party that has some nazi links (see the eloquent Dr Alice Weidel)
and are strongly anti-immigration, pro German (they quote Deutschland Über Alles) have a real stronghold here. Our kids have told us since starting at the Gymnasium, there have been multiple swastikas erased from around the school and lots of talks about how it is not tolerated, and then both our kids are coming home repeating such racist stuff. If this is happening in the Gymnasium, where parents generally tend to be tertiary educated and should know better, what is happening at the other high-schools?
And I have also noticed recently, whenever my kids and I go shopping and we speak English instead of German, heads turn, people stare and we are treated, very often, brusquely and rudely, which has never happened before. I would imagine this to be just a taste to what obviously foreign people experience daily. It makes me wonder what is coming and whether we are safe.
So, as to whether immigration has failed, I cannot say, but this anti-foreigner sentiment is being left to simmer. The AFD freaks me out, no matter how much my family and I joke about it.