Roving
I'm not sure the call is for a public inquiry, but a Fatal Accident Inquiry (the broad equivalent of a Coroner's Inquest) to hear the evidence. As Distant Voice has said, the Lord Advocate's office in Edinburgh has abrogated its responsibility to deceased servicemen for too long.
I agree about the speculation. One solution would be for MoD to release the tapes. I'm afraid MoD has a long history of releasing selected excerpts which distort events. This would probably upset families, but I can't speak for them. And nor does MoD.
Regarding Lord Philip, while he mentioned that the Air Marshals applied the wrong test, his central point was that the aircraft was not airworthy, and Air Vice Marshal Bagnall was not permitted to sign the Release to Service. MoD later conceded this, admitting that the aircraft only had a ground training and familiarisation clearance.
The link here to the Chinook case is the accident dates. It was claimed by Lord Philip and Government that the Marshals did not truly understand the legal test, while ignoring that the Senior Reviewing Officer (Wratten) was at the same time considering the Glen Ogle case, in which he clearly demonstrated he did understand the test. That is, he sought to apply his own test to Chinook, in an effort to justify his findings against the deceased pilots. As a barrister, you will know better than I how courts would view such actions, if carried out by civilians judges.
It is not widely known that these claims by MoD and Government were wholly refuted by the author of the test (Air Cdre D Hine) in written evidence to Lord Philip, when he reported that senior officers complained to him that the "no doubt" test was reducing their power. That Lord Philip omitted this evidence, and allowed Government to repeat the lies, was one of the least savoury aspects of his report.
Bottom line. Neither case is closed, because MoD and the state have not met legal obligations.