red button
I am no professional pilot. However, thirty years of flying have made me understand that there are moments when your brain is too busy with basic aircraft handling to perform additional flawless and logical analysis, regardless of training and experience. And there are moments when even an IR rated pilot does not look onto the ECAS or listen to some aural warnings. If the end of the runway is rapidly filling your windscreen for instance.
I am a pro in system engineering of computerized systems. As such, I am baffled to recognize that most guys in this thread after some 700 posts are still rather clueless as to what happens when auto this and that is selected and lever this and that is left where it should not be and auto such and such is inop and why it might be possible to have one engine screaming in reverse and the other trying full blast to keep the speed.
A logic that has so many interlocks is a feat to Murphy's law. Not because the logic is wrong, but because it is too sensitive to quirks and because it is far too complicated for troubleshooting when the going gets really rough and time (and runway) runs out.
In the industry we all now the red button for "emergency stop". I wonder if it would not be worthwhile to have such a button in the cockpit that activates whatever means are available to brake and dump lift and immediately stops whatever is trying to accelerate. Of course, it would require some basic interlocks too (like ground mode), but should remain fairly simple. And it would come in handy also on a rejected takeoff.
I know that the pro's do not like the "stop and think later" approach. But maybe it could save the day if the plane goes fast and the thinking slow.