There is no logic however, the original purpose of the CRI rating was to replace the TRI for single pilot aeroplanes. In essence this would be a company pilot conducting class and type conversions in an AOC environment where it was considered that such a person did not need to be a FI if they were experienced company pilots training other qualified pilots.
The privileges of the FI(R) were copied from the UK AFI rating and it was considered that they would only be conducting basic PPL training hence the need for a level of supervision. Any class rating conversions would most likely be in a club environment rather than a company environment. The original version of JAR-FCL 1 stated that the privileges of the FI(R) included those of a CRI (SE) but that disappeared quite early on.
Use of the CRI qualification in the UK has developed in a very different way to that anticipated and consequently, this anomaly has arisen. As nobody has raised the issue with the JAA it has not been considered in any of the NPAs. The same situation will exist under EASA-FCL so you now have an issue that you can raise as part of the current consultation.