Graceful Degredation.
After AF447 did Airbus modify the software for loss of speed sensors?
If the aircraft goes from 3 consistent indications to 2, to all different, then why cannot it not provide a warning along the lines of:
"Loss of one speed indicator, if another is lost then the AP will drop , set pitch and power and see you later"
Of course, it may be that you go immediately from 3 to none in which case there is no time for a long speech but even saying "AP dropout due to unreliable speed indications", gives you less surprises.
We must surely have the data to see how long it takes for loss of one speed indicator to all three inconsistent, who knows, it might even provide enough warning to start unloading the trim as well. What does the data say?