Theme Lambda probe, a question to our luminaries

I have a lot, a lot, a lot... very much read and experienced but there are still questions open, well actually I am ned much smarter!
The current discussion in the A8 Forum shows that it seems that it is difficult to mention facts here.

So now on the subject, let's assume first that the probe is OK and works properly.
In this case, this regulates the mixture in a certain speed range, this speed range seems to be a controversial issue, why?!?

In the second case, I assume the probe is not working properly. There are probably 1000 causes and even more.
Impacts, but this is not supposed to be relevant at the moment.

As a rule, we detect a defective probe at rubber-like/wave-like acceleration and increased consumption. We now know that this is not
the case is, at full load (so Konno). I want to believe this, because I can confirm this from my own experience (Imagination is also an education).
Also Konno's statement about the speed range I could explain to myself, because interestingly my car between 3 and 4000 rpm hardly any consumption differences
It is also known as the "F.A. 1l/100km -> between 120 and 180).

Now it's always advised to try and shut down the probe! But why? It was said several times that the ECU then works with the value 1
But what's the point? What is the physical background to this?
Furthermore, I would be interested if my observation would require less fuel than a broken physical proof of a clamped probe, and if so how?

I would now like to ask all those who think that I can also say something about not being able to do it and on the other hand, those who have not done it.
REALLY Know what to say. To sum up the question: How does a lambda probe work exactly ...

Thank you