controlled or uncontrolled
There is little likelihood that the aircraft was uncontrolled in the early stages of the flight. The track changes necessitated intervention at least to the time that the aircraft ended up south of Sumatra.
Thereafter the scenario established by the frequency shift has been used to suggest that the aircraft entered a rapid spiral descent which would be consistent with being uncontrolled and having TAC function for the first engine flame out and then freeze with the second flame out and loss of power. Perhaps. The doppler shift is also consistent with a course change in the time after the engine flame out, which would support intervention remained until later.
The flap fragment exhibited upward loading on the aft track area of the main flap element. That is inconsistent with a steep high speed impact into the water. It is consistent with a low speed imapct with partial flap or no flap deflection, at a high AOA, in near wings level flight. That does not support being uncontrolled. That flap track evidence is noted as existing in the report by ATSB, but then not commented on to explain it's anomalous condition. Under the circumstances that prevailed at that time, it is not surprising that some care would be taken on the analysis avoiding the inferences that arise from being controlled.
At the end of the flight, where does a person end up tracking the aircraft in the last 20 minutes of the flight? Continue directly on track, just keeping wings level, turn towards the sunrise, or turn towards the most important aspect of their spiritual life? There are really only 3 rational courses that the aircraft would have taken at that point in time, and they are all outside of the search area covered in the initial and the follow up search.
Blessings to all of the families involved in this tragedy. Aviation does not routinely have a loss from crew action, but it has happened in the past and in recent times. The human psyche is unfathomable, but human involvement in the operation remains the best solution for the state of technology that exists. The risks associated with a single crew member in the cockpit were recognised immediately that the enhanced security measures, both interim and permanent were instituted. To date, there have been multiple cases where the single occupant of the cockpit has ended badly, from A320, B737 and others. The desperately sad event of the Helios accident was a variant of this issue, and remains the greatest problem condition to deal with. At the operation I was with at 9/11, we established protocols to be followed to ensure a high level of safety as well as the security enhancement, but unfortunately that policy looks great on paper, but was disregarded more often than not as an inconvenience. We have a lot of improvements that can be made to protect the pax from the paradoxical issues arising from 9/11.