but I find it a bit strange that an aircraft with so many protections built in, will allow the autotrim to trim the stab into a position that you simply can't fly out of.
Since aircraft have grown in size beyond what the pilot can control by his own power, trim has always been a feature that can kill you if wrongly used. This was one of the reasons why the L1011 did not have a trimable horizontal stabilizer with an elevator, but an all flying tail. It was eliminating a possible risk. Due to the complexity of that type of pitch control, the concept was abandoned in favour of cheaper, lighter and simpler systems. Stabilizer trim requires appropriate trim setting, pilots and computers can mess that up (and did in the past). Autotrim is always designed for a certain purpose, and works perfectly for that. If you operate out of the design assumptions, the system can bite you. Even with autotrim installed, it is still the pilot who is responsible for the correct trim setting. Autotrim should assist him, not dominate him. It is the pilots fault if he lets it happen. It is the role of the pilot to check what his systems are doing. All the indications and warnings are there right in front of his eyes. The pilot should just not stop monitoring, which has never failed in all of his life...
Has anyone ever explained why AF447 PF obsessively pulled back?
I think this is pretty self explanatory for anyone who is able to fly an aircraft and read FDR plots in the report. The pilot did not obsessively pulled back unless the aircraft nose dropped by some 25 degrees (between 2:11:45 and 2:12:00, the normal behaviour of a stalled aircraft). However the normal behaviour of a trained pilot should have been different... But for a pilot in panic, pulling when your pitch is -10° is understandable, but should not happen. Especially if a synthetic voice is trying to point out an important detail for about a minute already...