Restricted FI(A) versus CRI
There are different national interpretations within JAR of these rules.
For example, Austria follows exactly your logic - an FI(A) is a superior qualification to a CRI. In Austria, once qualified on the type, and having acquired a minimum of 50 hours on it, you are automatically a CRI on that type - this seems very logical to me.
In France (and some other JAR countries), becoming a CRI requires an additional course (requiring payment of fees to the authority), even if your are already an FI(A).
To add to the confusion and lack of professional rigour, France reverts to Austrian logic for TRI qualifications - so if you are a FI(A) and have 200 hours on a type, you automatically become a TRI on that type. Only if you do not hold an FI(A) are you expected to acquire 600 hours on type, and also do some instructional training etc.