A complication in busy skies is the advisability of starting a max rate descent immediately after donning O2 masks. Excerpt from 'How To Do Well in the Sim'*:
When you call ‘MAYDAY’, if you're in busy airspace and you can get some sort of ATC clearance before you plummet, so much the better. It would be pointless doing the drill perfectly and then slamming into another aircraft beneath you on the way down. It's unlikely your TCAS will call out sensible RAs, nor those of nearby aircraft. The question is: ‘how long do I spend trying to get an emergency descent clearance before hypoxia begins to affect the passengers and cabin crew?’ And of course no-one can give you an answer – you must use your judgement as to when to start down if ATC can’t help.
This incident is another case of life (sadly) imitating art - the original draft of the novel 'Flight 935 Do You Read' (in which an airliner comes to grief after deliberate interference with the pressurisation system) was written in 1979-80.
*caveat: this article was written several years ago and procedures might have changed in the intervening period.