17,000 is not too low to recover from that. But I can’t imagine that they were in a flat spin all that way down unless pilots were doing something wrong.
They should have been able to at least turn the aircraft into a lawn dart -nose down. As that is the only real way to get out of that situation.
Aircraft of this type have variable pitch props. They can control the amount of bite the props take as they spin. Occasionally, the mechanics of those fail, possibly even reversing the pitch. That could be very bad, quickly. One prop doing what it should, the other generating no thrust or in reverse.
That could cause the tight flat spiral if they were trying to fix that issue and needing time to figure that out before lowering the nose. But turboprop engines themselves don’t fail too often so engine failure by itself doesn’t seem as likely.
I doubt it is was icing either. That wouldn’t affect just one side that much even at 17,000. The systems there are usually pretty good, and its Brazil - how cold and wet is it at 17,000’? This was big.
I am a general aviation pilot - 30 years worth. Though I have never piloted a twin or a turboprop.
I noticed the sound of the engines on one of the clips. It seemed unusual, more like a bat-bat-bat instead of the deep hum you would expect. I wonder if the pitch was wrong as you suggested.
Typically, it’s 5.5 degrees F per 1000 feet of elevation. So that means that at 17,000, it’s 93.5 degrees F cooler than it was at sea level. So if it was a hot day below, it was still 0F above.