Since the crew primary task then, is to try to regain control before anything else gets done, it is not surprising that distress calls were never made.
If situations can arise then, where using the radio to call a mayday is not possible due to the work load in the cabin, then its time voice activated radio was introduced, if not one simple button to send a distress message.
To not be able to transmit in an emergency situation is a serious flaw that needs to be corrected.