As to a CVR helping....oh yes indeed it would.
If all crew stations were monitored and we had the last thirty minutes of conversations amongst the Crew....we would know a great deal about their thinking re Tasking and any discussion the Crew about them.
I am quite sure there was some discussion by the Crew during the Flight and it would certainly give us far more insight into decisions made by the Crew that night.
We pretty much know "What" happened....but we are far from knowing "Why".
We would also know of any discussion about Warning/Cautions or fuel state.
We would have an audio record of any discussion about Emergency Actions such as landing out or diverting to a safe landing area.
Very adamantly I support the noting that a CVR would have provided much information that would go towards answering the "Why" part of this Investigation.