The single most cause of limb injury in climbing and all other dynamic sports (not including fall injuries) is poor core conditioning and lack of core strength.
OB Juan,
I don't want you to interpret this as an attack.
However, your initial supposition is one that I don't think is accurate.
I understand that you are an AT-C? And I assume you work with PT's and Dr. Ireland and have other experience in sports medicine.
A few of the most common climbing injuries are 1. A-1/ A-2 or cruciate pulley strains. 2. FDP/ FDS(flexor tendons of the fingers) tendon strains/ ruptures. 3. Rotator Cuff injuries (Supra Spinatus probably being 90% of these. 4. Long Head of the Biceps inj. and accompanying SLAP tears of the labrum. 5. Medial and Lateral Epicondylitis. 6. Retinacula strains of the wrist. 7. other odd tendonopathies of the wrist (TFCC inj).
I don't know the specific order of these, but for sure the pulley injuries are #1.
These are all upper extremity injuries, and in none of these would I say lack of core strength resulting in a relative loss of core stability was a direct causative factor in these injuries. Contributing, perhaps, but the cause of these injuries would be from, as you correctly stated, dynamic eccentric, or plyometric loading of the muscle belly, tendon, enthesis, etc... (what ever body part in involved).
I think your intent to educate about core stability in climbing is worthy and needed. It is sports like climbing and gymnastics where we turn the kinetic chain on its head. The fixed anchor point of contact to terra firma, which is usually the feet with everything else being connected in muscle and tendon chain to the feet in normal everyday walking about, suddenly becomes very small areas on the tips of our fingers. The kinetic chain suddenly has to find anchor here on these tip pads and the body, which usually has the huge muscle groups of the lower ext and pelvis to control the body mass, has to use the forearms, upper arms, shoulder girdle, etc... to control the body mass' movement.
In this scenario, especially on steep routes, the core strength is key to controlling body movement. This core strength provides the platform stability by virtue of its connection through closed kinetic chain to the finger tips to check dynamic swinging of the body and the subsequent out -of -control loading of vulnerable joints.
For instance, when 180 lbs of body mass swings with a velocity and acceleration through space only to come to a sudden stop by the poor RC and capsule, the result is rarely good. Just ask RHunt. In these instances core strength and stability would help reign in out-of-control body mass swing and thus prevent the development of the conditions needed to cause these upper extremity injuries. Therefore, weakness of core musculature and lack of core stability would be considered a contributing factor in creating the conditions that would allow dynamic injurious loading of a joint/ connective tissue. (sorry Rhunt. I know you have abs of steel).
Maybe this is what you where driving at. But, the direct cause of injury to these upper ext body parts would be the overwhelming force of the body mass accelerating through space meeting the meager resistance of small inadequate upper extremity muscles and connective tissue that are trying to protect the joint, followed by the sickening bowstring twang of rupturing.
that is what I think.
Is core strengthening going to improve one's climbing. Very much. Having a good stiff core is like having a good aluminum bike frame. It is very stiff and helps transmit the force created in the crank to the back wheel most efficeintly with little loss of energy in the flex of the frame. (that kind of works).