Understanding the layers in CNN
This is a good question to ask as it pertains to important neural network concepts.

&quot;Why don't we have several separate layers, each of which does a
specific extraction of some features and once all the needed has been
extracted&quot;

The answer is two-fold.
First, the layers depend on each other. The reason deeper layers can extract higher-level features is that they build upon the lower features extracted in the earlier layers. The layers may be different in architecture but they could simply be the same layer duplicated multiple times and initialized with the same weights.
Second, it is important to understand that the layers are not &quot;told&quot; what type of features to extract. Realizing that each layers represented various level of features was very important in better understanding the behaviour of neural networks and to confirm that no, it isn't all black magic. And it is important to understand that is a learning artefact which may not always occur depending on the network, data, and training strategy involved.