As a very amateur rock climber I can have a stab at this. I am naturally hypermobile. Though mobility is an obvious advantage, climbing requires a good ratio of strength and control of movement and I'm sure promotes good proprioception. I've never found a problem with it in that sense. Injuries tend mostly to be related to carelessness aproaching or leaving the crag more than actual climbing! However, with 'fanatical' climbers, overuse or repetative strain can cause problems - noteably to my knowledge problems with brachioradialis (lifting bodyweight in pronation so not benefitting from the power of biceps) and I have treated a few climbers with swan necking and boutonniers who have required hand surgery. As to wether strapping helps I can't really comment as I've never tried. But have seen articals in climbing magazines in which climbers themselves have devised strapping for the forearm muscles with anecdotally good results!