So we made successful descent into semantics, namely what does "failure" actually mean.
My viewpoint is that CS 25, applied to measuring systems, refers to failure in strict sense: measured output being nonexistent or obviously out of realistic range (e.g. AoA of 400 degrees). Those can be easily detected without any crosschecking. Failure in broader sense of "not fulfilling the intended function" might be impossible to detect without being aware of the big picture and realizing which details don't fit. Despite its shortcomings, I do maintain that this task is (for the time being) better left to head mounted computer.
Now you've mentioned them, there is very significant difference between Birgenair and Aeroperu. Despite having only one pitot blocked, Birgenair crew has inexplicably decided to put its faith into the only datum in cockpit that was wrong. Simple crosschecking of two remaining ASIs would show that no1 ASI was at fault, if its failure during T/O wasn't hint enough. Aeroperu crew was deprived of each and every source of static pressure so simple crosscheck wouldn't do. That they were bombarded by alerts for faults that were nonexistent did not help their situational awareness at all.