This is just bad handling of an aircraft, pure and simple. Such incidents need genuine pilots, as the term defines.
Now the eternal question is why there were none present and how to remedy the situation.
In my humble opinion the remedy is only training and experience by exposure. But REAL training and not the actual placebo sim scenarios everyone can look into and prepare beforehand. They only please regulations but not real life. Pilots need to regain (or worse: aquire) piloting skills again.
The basic skill required here is: AP/AT off, wings level, pitch + power, then control the speed ….. It’s commonly called flying.
I don’t like the cries for another automatic feature. They can fail to engage, the AP can just throw it back to you because it does no recognise any valid mode or the AT can be engaged but refuses to act etc. etc. In all those cases it’s back to square one, meaning YOU will have to FLY it all over again.
I don’t like the cries for more drills or memory items. There are too many already. Quite often they are somewhat contradictory and more often than not they are prone to changes by rocket-science blessed chief instructors.
In case of confusion or startle, the human being is mostly only able to repeat two or three very simple, trained actions, which again is commonly called flying, but not the myriad of brilliantly crafted multiple step procedures on the 50+ pages in the QRH. They can be skilfully memorised and regurgitated, but it’s way more difficult to apply them correctly when needed. QED.