@Franzl
Autotrim is a separate system from the protections and the autoflight, as such under manual control and without protections it does exactly what the pilot commands. It does exactly what it says on the tin and trims automatically in the same way that manual trim is applied on older aircraft - there have never been any hard limits on manual trim wheels, why should there be one on their modern automatic descendents?
In this case we have one incident where possibly as a result of panic or poor training the PF commanded the autotrim - *after* the aircraft had already stalled - into an inappropriate position. I can say with some confidence that had the PF realised what was happening and pushed forward for an equivalent time to the amount he had previously been pulling back, the trim would have righted and control would have been regained. One incident in however many tens or hundreds of thousands of flights that this type and it's sister ships have made safely and without incident every day.
As such, it's far more realistic to train pilots to understand what the autotrim does as part of their type conversion (over and above never making and holding large control inputs for more than a second or two) than it is to redesign a system that works as well, if not better that it's manual predecessors and end up sacrificing pilot authority in the process.
@infrequentflyer789 - While you are correct in asserting that one should not hear the Stall Warning in Normal Law, and as such hearing it is an indication that something has gone wrong - as I understand it, the warning and annunciator system is not directly connected to the flight control logic - so it is never switched off or suppressed by anything directly. The FCU is a network of loosely-coupled, real-time processes with a degree of redundancy built in - not a monolithic, closely-coupled design.