Transasia crash

It has now been confirmed that the pilot first throttled back and then shut down the LH engine after a master warning had appeared relating to the RH engine.
After a couple of minutes the RH engine duly auto feathered as it ran down. The crew did attempt to restart the LH engine.

It does seem extraordinary that this sort of mistake can still be made. It has certainly happened before - East Midland crash?
After all the on board computer knew which engine was failing so you would have thought it would at the very least have given a positive warning that the pilots action was depriving the plane of all power.

Cockpit interaction between the two pilots in a commercial aircraft was radically changed after the Manchester crash. It is now a requirement for the non-handling pilot to confirm the failure and action with the handling pilot before carrying out the action.

So, either they were not following procedure.....or they both got it wrong................ or it was a software issue that had not been foreseen...........or something else. Either way, it's probably best not to conject until after the accident report has been made public.

Somewhat surprisingly the output from the flight data recorder has apparently been released.
Link
You certainly would not expect the AAIB to publish anything until a formal report was released. Perhaps they do things differently in Taiwan.

I think the Taiwan regulators are under serious pressure to make the reasons for this accident visible to the public, as it should not have been an accident in the first place, the ATR is capable of flying on one engine, as are all other twin engine aircraft in this size category.

Having said that, from conversations with a (now retired) ATR captain, the ATR can be a handful in some circumstances, so if one or more of the crew were new to the type, (while all 3 had a lot of experience, their time on type has not been revealed), that may be a factor in the manner in which the failure was managed.

What's even more damning is that 10 of 48 pilots who were given oral competency tests on engine failure procedures by the regulators have failed that test, and been grounded. Another significant number were either "ill" or "travelling" so unable to take the test, and also grounded until such time as they pass the test.

The full reasons for the decisions to shut down the wrong engine may never be completely clear, but with 3 pilots on the flight deck, there have to be some serious questions about the way that the Asian airlines operate their CRM policies, as there have been a number of similar incidents in that part of the world, and cultural aspects of the "loss of face" for the captain have been identified as a significant issue in the subsequent reports.
It's very possible that reducing the power on the good engine made the aircraft easier to handle, as it would have reduced the asymmetric thrust issues, but an easier to handle aircraft that's only going down is no solution to adequate training and awareness. Hopefully, the eventual full accident report will determine all the issues, and issue appropriate recommendations that will help reduce the risk of a repeat.