Watch any level of organised basketball for a few minutes and the same action keeps appearing. One player holds the ball, a teammate walks up and stands next to the defender guarding him, and the two of them attack the space that opens. It is the most common deliberate action in the sport, at youth level and at the top of the professional game, and its dominance is not a matter of fashion.
The pick-and-roll persists because of what it does to a defence's decision-making. Most offensive concepts try to create a shot. A screen creates a question, forces two defenders to answer it together and under time pressure, and then punishes whichever answer they choose. Understanding why it became the default means starting with the geometry and following the chain of consequences.
