Part of the reason German internet is slow is because German telecom didn't want to invest in fiber. And arguably had it remained a state monopoly they also didn't want to do it. They spent a lot of time on super-vectoring and all this copper optimization.

Now if the German government had forced and paid for the needed investment to upgrade Germany to fiber quickly, yes such a monopoly could have done it quickly. But it seems unlikely to me that this would have happened as an alternative to privatization.

That's always the thing with government run, you can just assume that the government run thing would have done the smartest best possible thing. But this is not always the case and depends on many factors.

Arguably the privatization was better then a badly run monopoly. At lest this way in some regions people could escape the monopoly better.