Respectfully Hamish, that's exactly who should be doing it.
There is an obligation mandated by QR&O 4.02 (respecting officers) and 5.01 (respecting NCMs) to report infringements of the law etc to the appropriate authorities. QR&O 106.02 requires that: "Where a complaint is made or where there are other reasons to believe that a service offence may have been committed, an investigation shall be conducted as soon as practical to determine whether there are sufficient grounds to justify the laying of a charge."
I think that's both a clear cut and an absolutely necessary requirement.
Where people may honestly differ is the question of whether or not specific actions constitute a crime. I expect that few of us would argue about what the extreme cases (for example Staff Sergeant Bales murder of 16 Afghan civilians in Panjwayi in 2012). Where the difficulty lies is in those grey area cases where one can't easily determine whether actions taken were appropriate or illegal in the circumstances. For example, from what I can parse of the evidence, Lorance, ordered fire on three civilians who were showing neither hostile acts nor hostile intent. He did this principally on his belief that Afghans on motorcycles were spotters for the Taliban. This was contrary to the ROE in effect and it was his own soldiers, the ones he said he was trying to protect, who reported the incident to the CoC.
Wouldn't you agree that this was their obligation under military law? And also that once the report was made that it was the duty of the CoC to direct an investigation and to subsequently lay charges?