When I asked one of the coaches why they don't do much "cool down" stretching, they simply said, they just never do. So tradition, as RBW points out, does play a key role in training.
In the mean time, I've been encouraging Nastia to do her static stretches after class while she's still warm in addition to the pre-workout warm up. Even she now understands that they are MUCH easier to do when your tired and her range of motion is dramtically increased during the stretch.
I love you dedication. I applaud your focus on educating yourself about gymnastics and trying to help your dd. But what happens if "in the mean time" doesn't stop? How much time should parents have to devote to "monitoring" or "correcting" issues that are occuring in the gym related to the training program the coaches are using.
After nearly 5 years of dd attending practices, I have come to the conclusion that this should not be necessary. What are we really paying for? If we ourselves have to become experts on gymnastics, aren't we setting a low expectation of our coaches? I believe there are coaches who do educate themselves and hold themselves to a high standard. Unfortunately, they may not bring all the "hardware" that we as parents can be sucked in by.