Yes, these systems generally work well and I am not trying to advocate ignoring them.
The exceptions cited are quite rare, but far from remote. Every now and then it's plainly obvious the computer has gone haywire, or its output is not relevant under prevailing circumstances. What I'm against is following the computer slavishly, even when it obviously doesn't make sense. The FAA stance on TCAS quoted earlier seems to be in accordance with that.
As for the EK777 at DXB. Yes, it was a mis-handled g/a. However, the whole event was triggered by "long flare" warning issued at ~1000m deep into a 4000m runway. Was it a cause of the accident? No. A contributing factor? Yes, in my opinion at least. What would have happened, had the crew continued the landing? Nothing.