Indeed. It is quite a plausible scenario for a shredded tyre to result in further problems, e.g. hydraulic line failure from said tyre debris. That said, I acknowledge that there are some "old school" instructor types out there who think the only way to do their jobs is to load the student up with problem after problem after problem - until they snap. This is not a realistic situation, and the sooner these people hang up their hats, the better.
Training and checking is all just part of the job description, and as long as one continues to work in this industry, it's just one of those things we all have to put up with. However the best operators recognise that the environment should be more "T" and less "C."