I think there's a certain inverse relationship between flexibility and strength. "Muscle Bound".
At the Bikram Yoga studio, I've learned to tell what other disciplines people are probably doing, based on how they perform in certain postures. This time of year, for example, we're innundated with the Nutcracker Ballerinas who come into town from all over to fill the various Nutcracker casts. They're extemely flexible but obviously not used to the postures. They'll do the posture slightly incorrectly, but go far deeper than I could on my best day. Incredibly, they wilt around 45 minutes into the practice. You would think they'd have more stamina.
To be involved in sports, you need flexibility, strength and endurance. In varying degrees depending on sport. For climbing you'd need all three. So you'd have to have a flexibility component in your training.