Back in the 60's part of the training at Hamble was a visit to the decompression chamber.
In the 35 years that followed in BEA/BA never had an engine failure but had three emergency descents. The hypoxia training taught me, especially on a two crew aircraft, that playing with the system in manual mode that took the total attention of one pilot was a non-starter. Any failure in auto mode get down into the thick air and let the engineers play with it.
We may never know what was going on in the Socata but why was there no urgency with regard to the descent request. The odd "magic" word would at least have got the controller "in the loop"