Telling someone on the ground about your situation takes a back seat to flying the aircraft. The workload of the crew must have been overwhelming so it’s hardly surprising that a Mayday call was missed.
As stated above, radar has changed everything in the last few decades, previously a position report and description of the problem would make a critical difference in search and rescue knowing where to look. In this case the controller could see the aircraft going down and could give SAR a good starting point.