Man, all of those advocating arm braces need to learn some basic physiology and physics. If you're able to totally immobilise the arm and elbow joint (i.e. make the arm rigidly straight), the pressure being put upon the area by movement of the arm in bowling would result in injury. Why? The joint is full of fluid parcels and flexible tissue; that force generated by the arm's momentum has to go somewhere and instead of being dissipated by natural flexibility in joint, it would put shear movement pressure on the bones and if you bowl fast enough, probably go a long way towards bursitis in the joint (elbow and shoulder would be my guess). The biceps would be fully extended and the triceps slack so force would transfer straight to the nearest joints/pivot points; i.e. the elbow and shoulder.
And let's not forget that when you immobilise an area, stabiliser muscles and ligaments pick up the slack. The muscles aren't anywhere near as strong as the bicep/tricep muscles but they're stronger than the ligaments and I'd imagine, without flexibility, the ligaments would be shredded by the pressure transferred by the stabilisers. The immobilisation of the elbow would also put a great deal more pressure on the shoulder muscles and they wouldn't last long (for the above reasons; shoulder ligaments aren't super-strong and do a lot of work anyway). A lot more of the bowling momentum would come from rotation of the shoulder (rather than use of the much stronger chest muscles) again, causing many physical problems.
Yes small amounts of damage are caused by the flexion in joints but they're flexible and that flexibility is what allows the force to be spread evenly so that damage is limited to micro-tears in many places as opposed to big tears in few places in an immobilised joint.
In weight training, it's similar to the difference between isolation exercises and muscle 'recruitment' (compound exercises). I've been doing weight training for some time now and isolation exercises (where you immobilise as many parts of your body as you can to exercise one muscle group) always cause more injuries. Why? In muscle development, muscle tearing from doing work causes muscle growth in the rebuilding process when it comes to rest. It's just the way bodies work. So when you isolate muscles, all of the force of the weight hits that area only so you get greater numbers of micro-tears (and therefore muscle build-up) but a greater chance of injury if your technique isn't quite right and (most importantly) the pressure on your joints is much, much greater. Why? The force from the weight hits the muscle, yes, but as soon as the muscle starts to fatigue, the joints and stabilisers take progressively more and more of the mass so you can continue to support it (after all, there are fewer muscle groups available to 'recruit'). It's why isolation exercises are so dangerous if your technique isn't up to scratch. Examples of this sort of exercise are things like bicep curls on the machine where you rest your elbows on a platform and full extend your arms downwards, grab the weight and then pull upwards to your chest.
In the opposite case, such as in chest exercises like bench-presses, the reason why few injuries are ever done on the bench is because when you lift a weight like that, the weight is, maybe 70% supported by chest muscles but the rest is supported by biceps, triceps, shoulders and a little bit of the abs. In effect, more muscles are 'recuited' to do the job (lift the heavy weight). So muscle bulk gains are slightly less than isolation exercises but overstrength is greater and the chance of injury is much less.
So yeah, immobilising joints under stress would likely cause some pretty serious injuries even if there was specific strength-training to build up areas surrounding it.