With the exception of eights, I've regularly used most of the maneuvers as part of my paid flying for many years...they have had extensive practical applications.
For you as the budding commercial pilot, however, they are exercises and demonstrations of basic flying skills. The Chandelle, for example, isn't a maneuver designed to teach you to escape a box canyon. If you fly into a box canyon without an out, you probably deserve to die. And there are far more important tactics to get out than a chandelle.
It's a maneuver that teaches you to coordinate airspeed with changing pitch and bank angles, nothing more. It's often taught as horsing the nose up and running out of airspeed when you've turned a hundred eighty degrees, but that's not it at all. Rolling into the turn smoothly and accurately such that you continuously increase your bank for half of the maneuver, and continuously decrease it for the other half requires coordination. More so considering the changing control forces, and decreasing airspeed. Properly done, your pitch increases continuously from the start of the maneuver until half way through, and then holds constant. It must achieve a pitch attitude that allows for the airspeed to bleed to minimum controllable at the same tiem you arrive at the conclusion of the maneuver, just as the wings roll level, just as you reach one hundred eighty degrees from the start.
Likewise a Lazy eight has numerous applications, but more importantly, teaches you and requires you to demonstrate coordination. It's a simple maneuver, but a good training maneuver, and I've been required to demonstrate it on checkrides ranging from small single engine airplanes to large four engine airplanes. Often in the field I use a combination of a lazy eight, turns on or about points, and a chandelle in typical maneuvering close to the surface, all with eyes outside the cockpit. Having an understanding and feel of the airplane is important, and the classroom maneuvers and concepts find a very real application in day to day flying for some jobs.
Your requirement to learn and demonstrate them isn't designed to prepare you for those jobs, however...it's intrinsic to your basic flight training and your bag of elementary skills.
Really training out to include basic aerobatics too, but sadly it does not.