@ RR_NDB:
While I agree that the system could also provide good news to the crew, I don't think your example is pertinent.
Indeed, the system has to be sure of itself to provide news (particularly good news such as: you now can rely on...)
The current logic is: The fact that the 3 airspeed sources give ~ the same value is an indication that this value is correct as long as no error occured.
As soon as an error occured (and until a system reset on the ground, with a check of its sources), the system is no more able to determine if what it "senses" is true or not.
You can easily imagine that 3 frozen/clogged pitots will at some time indicate ~ the same (incorrect) airspeed value. It would be very dangerous to rely on that (incorrect) value.
I know that ice eventually melt, but ice is not the only potential problem encountered by the pitots. What about volcanic ashes, for example?
Hence it's far safer IMO to let the crew do its job, as pilots: Assess the failure, eventually see that the values seem correct again and decide to give them (or not) (limited) confidence. In the mean time, fly pitch&power, which can be done without relying on airspeed indications.
Regards.