Assume they were wearing their masks, if they had previously made a PA should they have taken their masks off and used the hand mic like you suggest?
If you are about to say well why did they make a PA prior to a mayday? Maybe they were going the right way, at the FL they wanted and had no restrictions on speed.
In my company we did it like this.... I would have done......Can avoid this by......
They are safe on the ground, who cares what you would have done!