Sad situation... there is a chance that by the time the pilot realised there was a pressurisation problem in the aircraft, he was already suffering the early effects of hypoxia. Had he been fully alert he might have called a pan-pan or a mayday... but sadly he did not.
I do wonder though, if the controller should have at least asked if the pilot if he wanted to declare a pan pan or mayday. It might have prompted the pilot to declare and emergency (which we know now, it was). In the minute or so of consciousness the pilot might have had left, he might have been able to set up for a decent and the controller could have got on with clearing other traffic. It does look like the controller either did not realise the seriousness of the situation, or decided to take the easy option.