The issue about turning is long established and is only in part related to traffic avoidance.
If you want to descend in an expeditious manner do you;
a) shove the control column forward and change the loading by the maximum negative amount until the desired attitude is reached; or
b) roll the aircraft which will then all by itself lower the nose while maintaining 1g, trim as you go and smoothly level the wings in the new nose low attitude.?
Basic flying which is more gentle on the aircraft.
The argument about traffic below and going straight or turning has little relevance in domestic airspace since there is little point avoiding the parallel traffic simply to survive long enough to spear a crosser. Or cause a break-up by bunting the aircraft unnecessarily as per UK procedure.
With no pax on board and FL350 or less (depending on type) then as SNS3Guppy says once on oxygen and stable whats the point in rushing. There is as they quite also correctly point out 2 situations - with suspected structural damage and the alternative - system failure causing rapidly increasing cabin alt. Each requiring very different process.
With pax on board then pay heed to the fact that FL250 is the max for the rubber jungle being used for an entended period but - also no point in them being concious and breathing passing 10,000 if you have broken the aircraft entering the descent.
My opinion;
Crew Oxygen,
Internal communications,
Passenger Oxygen,
Descent - using the smallest change in g possible i.e. in most cases a gentle roll and allow the nose to drop. Situational awareness - Alps etc don't go for 10,000 in the alt sel. South China etc go for escape route.
7700 - it is in the checklist and as said above everyone in range gets an alarm and/or filter breakthrough.
Our job is to ensure the safety of our aircraft. I don't at that stage worry about anyone that is no on board our aircraft.
Mayday call when it is the next priority.