Competition horses, such as eventing horses and show jumping horses, that are running and jumping at speed on different terrains like grass or mud, need to be shod and have studs or caulks to prevent slipping and reduce the risk of a fall. Corrective shoeing is also a whole other category. Example, I've seen foals born with contracted tendons and trimming was not enough.
Actually, today unshod horse are competing in events from cross country and endurance to stadium jumping as more people are starting to realize that it's best for the horse (even if some events are not good for the joints, but that's a different issue). If the extra traction that cleated shoes provide is needed those riders are using boots to provide it (while still allowing the foot to function normally, but still creating the extra joint strain in cases where it applies).
As for contracted tendons requiring a horse to be shod that's the same story they give for sever laminitis ("no trim is going to fix that"). No one is saying a "trim" will cure everything, but there are a lot of ways to treat something (successfully) without shoeing. People who deal only with doing things unshod have a lot more to draw on than just a trim (e.g. Boots, casting, etc, etc...). There are horses that were "beyond help" and told to be put down when shoeing failed to fix the problem and yet they became sound again without shoes. It's not easy. It's not quick. And if you're paying for it it's not cheap, but horses that the a vet and farrier failed some how managed to survive with an unshod treatment and different vet.
Until I hear Dr Stasser or even Claudia Garner tell me that they've encountered a case that must be shod (I've seen the results of their work) I'll stay with the unshod solutions . So far it's worked best for my horses and the ones I've helped. The problems with shoeing is a bit overwhelming. All the issues created by shoeing makes me glad that I never had to make the change (many thanks to my grandfather).