If you do not use the wave of extension, you often push through the foot and leg to stand as you pull with the arm. The pull with the arm actually begins to pull weight off the feet and load the arms with more of your body weight. This means your upper arms, grip and back and shoulders have to work harder.
Don't believe me - try campussing and see if it is harder than using feet. Or try doing pull ups without any movement through the torso - just a straight arm pull. Then allow the movement to flow through the body as you pull up.
In my book, Climbing Your Best, published in 2001, I wrote the following about the wave of extension...
" A key part of efficiency in movement is maintaining the momentum carried from one hold to the next."
How to Practice
One of the best practices to make you practice this skill is to climb with straight arms in slow motion.
Best not to follow a route and use really good handholds as you try this initially. If your gym doesn't have enough hold options, try this on easy for you routes. Open the foothold options because you will need to try to find balance as you climb through slow motion. When I ask for straight arms, what I mean is that as the left arm reaches, the right arm is relatively straight. And vice versa. In slow motion, you will notice you need to use your core to stay close to the wall. Try it. Send your questions, I would love to hear from you.