It is indeed, but according to the article, the Taipei pilot had five thousand hours of flight experience. If five thousand hours of experience is not sufficient answer, it's time to reevaluate the question.
There's a saying in aviation that one pilot may have a thousand hours of experience, while another pilot may merely have a hundred hours of experience repeated ten times.
Capt. Sully is known for being involved in aviation safety before Flight 1549 put him on the front page. It was like decades of training and experience, was leading up to that one day in January 2009 when Flight 1549 was able to land safely in the Hudson.
Some career pilots have very little stick-and-rudder (& thrust lever) experience, and fly on autopilot for thousands of hours. Shutting down the wrong engine is either very poor piloting, or a systemic training issue.
I believe the true failure here wasn't shutting down the wrong engine, but trying to shut down the bad engine at all while still so low. Shutting down a failed engine is not a priority. It can windmill and tear itself to shreds for a little bit while you keep the airplane flying, get to a safe altitude, and figure out what to do. Multi-engine pilots I've talked to about this have said that it's standard procedure not to shut down a bad engine below a certain altitude, precisely so you're not screwed if you go for the wrong one by accident.
A common cause of aviation accidents is a pilot responding to an emergency by making it worse. A safety class I went through recently presented a case where a pilot thought he was low on fuel, decided to land at a nearby airport, botched the landing by coming in high, fast, and downwind, and crashed off the end of the runway. Turned out the fuel gauge was faulty. There's a famous C-5 crash that's similar to this Taipei crash, in which an engine failed, the pilot shut down the opposite engine by mistake, and then botched the landing because he flew as if he still had three engines instead of two. A semi-frequent cause of glider crashes is a pilot failing to lock their canopy which then comes open in flight, and the pilot tries to fix it instead of flying the airplane. They key isn't to ensure you do the right thing fast, but to make sure you prioritize and don't do anything fast that isn't immediately necessary. Engines fail? Find a spot to land, right now. One engine fails? Keep climbing and breathe, then take your time to decide what to do next.
Certified passenger turboprop aircraft (ATR-72 included) should be able to maintain altitude, without feathering the failed engine.
I was thinking of British Midlands flight 92, where an experienced crew that were new to the 737-400 misread the vibration instruments, and shut down the wrong engine, at altitude. Poor training on the -400 differences was a major factor.
Experienced pilots do screw up occasionally, but good CRM usually avoids a mistake snowballing into a fatal crash.
In a Cessna 150, I had the window come open on takeoff. Same aircraft, same instructor, same thing happened to my dad years before. He told my dad to "Fly the plane".. I knew not to close the window until at a safe altitude. He just smirked a little.
That's not quite what happened. The vibration instruments on earlier models were known to be unreliable, so the pilot tried to figure out which engine had failed using other indications (I forget which).