why can't he teach someone who already has a licence - unsupervised?
What are you going to teach them that requires you to hold an FI or a CRI rating?
Have a look at the very first paragraph of JAR-FCL Subpart H - Instructor Ratings. Are you going to be carrying out flight instruction for the issue of a pilot licence or rating?
No?
Then you don't even need an instructor rating to do it.
The flight will of course not count towards the experience you require to have the rating unrestricted, the other pilot can not use it as the 1 hour with an instructor for rating revalidation and checking the insurance would be a good idea...........oh, and unless you are acting as safety pilot while the other pilot flies under the hood, it is strictly a single pilot operation so only one of you is going to be able to log the flight time.
All the training for which one is required to hold an FI or CRI or TRI rating must be completed at an RTF or FTO or TRTO as appropriate. What restricting the FI rating does from a practical point of view is prevent the new FI from starting their own RTF and offering services on their own. The CRI however does not have such a restriction and there is no requirement to have one.