The only way to train your muscles is to over-load them. By using a technique that uses time as a control measure, and telling soldiers to go to their knees but keep going, the PT instructor is using a virtually foolproof way to ensure that the soldiers will end the set laying on the ground, thoroughly exhausted. Muscle failure means exhaustion. Then go back and work the push-up muscles to exhaustion again. Some personnel seem to have a hard time understanding how to get the necessary intensity so that adaptation occurs and, two weeks later, a soldier can have more muscular endurance.
Lets compare five sets of push-ups to exhaustion vs. the descending sets.
You tell your group that they will be doing five timed sets of push-ups to exhaustion. Once they can't do another correct push-up they are to go to their knees and continue until they collapse. Between each exercise you do something different so the push-up muscles can recover. In contrast to your group, I tell my group that we are going to do descending sets of push-ups. Between sets we also do another exercise for recovery.