Oops, to add a CRI can become an Examiner but not for a PPL flight test. As you say how can you test something you have never taught.
I know of a lot of clubs who are going towards the CRI as they can have PPL Instructors for doing the tailwheel and club checkouts, etc and FI's dedicated to Ab initio training. A CRI who does nothing but fly tailwheel cubs for example can often make a much better tail wheel instructor than an FI who just spends his life in a 152. The student gains out of having someone who excels in one particular area rather than being a jack of all trades.
If a school can't manage its bookings to get the right Instructor for the job its a poor show. I assume on that basis that all of the Instructors also have to be examiners to make sure there are no mistakes when a test is needed......