Shaping the shot and trajectory are surely part of a refined game, and these shot qualities are part of the real difference in a great game versus just a good game. The shape of the green and pin position dictate the shape and trajectory one should try to command, and the reason is your good shots will be really good and your misses will be pretty good and leave par a real chance.
Consider a narrow green that is angled so the left front is closer and the right back is angled about 45 degrees deeper. Then put a water hazard in front (think about 12 at Augusta, ) and a trap along the back. Unless the pin is front left, the best approach is almost always a cut shot, moving left to right. Aim a little left of the pin and if you hit it straight, you hit the green, if you hit a slight draw, you are not wet, and if you make the shot, you have a birdie possibility from pretty close. A cut tends to track down the center line of the green. A draw risks too much. The distance must be perfect, push it and you are in the water or over draw it the ball goes in the trap. Draws run out a little further in general. So pick a club that will get the ball on the green with a normal cut and hit with confidence... a little miss will not hurt you.
The opposite situation can be in play just as easily, depending on angle of the green, taps and hazards, and preferred landing areas. A deep left pin usually begs for a little draw back into the pin.
But the real reason you need to know both shot shapes is when you are choking or a little off your game. You can hit a shot that moves away from the trouble that could make a big number.
I love greens that are designed to make you consider your options and play the optimal shot to improve your chances. To me that is the most enjoyable part of golf -- the chess match between the designer, the pin placement of the day, and the golfer.