To quote Superpilot:
'We need to determine the nature of the spurious warnings quickly and to do that we have a whole plethora of inputs and sensors to give an indication of airspeed. Diagnosis is required and suitable action after that. This is what the Airbus AD seeks to achieve.'
I can definitely see the good in the system you delineate however there is also the fact of diagnosis requiring time.
Just to reference as an example the Quantas A380 incident at Changi in 2010...and the pages and pages of warning notifications that the FO had to read through, unable to triage the indications as each had to be read and processed before the next could be dealt with or even seen - they made it and they were extremely fortunate to but in many situations, time is absolutely not available for this task.
When you have a loss of hydraulics and flight controls the last thing you need is possibly a freaking out ECAM delivering you 75 million messages at once. But unfortunately that's what you get.
I don't know however if the EICAS system provides any more flexibility than this though I'm aware the format is different.