The most important reason to map the PoPs and the LoAs, is that it will put you on the track of pieces that are partly immobilized due to their Fun(ction).
Function is different. It can't be seen with your physical eyes. You can only see it with your minds eye. And that can give you an edge. In case of function, what you see with your physical eyes, is in contradiction with what you see with your minds eye. With your physical eyes, you see a knight that can hop around in a knightly manner, as knights do. But in the realm of Functionality, the knight is bound to the protection of h7 and d7.
We have to develop a mental eye for the partial immobility due to Function. I write Function with a capital, in order to show that we are talking about the functional motif. We must learn the different methods how to exploit those partial immobilities.
|Black to move|
qr4k1/2Q1pp1p/6p1/r1nb4/P7/4PNP1/5PBP/R2R2K1 b - - 1 1
Black wants to take the knight on f3. For the physical eyes, it looks as if the black queen is participating in the attack on f3. But the mental eye sees that the black queen is bound to its Functions: defending both rooks and the bishop. The black queen is immobile, and hence isn't participating in the attack. The black rook is bound to the defense of c5, so it is immobile too.
Logical thinking in chess starts here. It starts with the Fun. Use PoPs and LoAs to lead you to the Fun. Chess thinking starts with thinking how to exploit (enemy pieces) and how to minimize (own piece) the immobilities. In this specific case, black wants to free its queen with tempo from its duties. So that the black queen can really participate in the attack on f3. Of course black must give white no chance to protect his knight.
Chess thinking starts with the Fun. The Fun starts with PoPs and LoAs.