I wish...
In fact this is how AF447 crashed... a plane under direct control of pilots...
Read: https://www.vanityfair.com/news/business/2014/10/air-france-...
Also, when they went very far into stall, the stall warning disabled under the assumption it was a sensor problem rather than the airplane actually getting into that bad of a stall. So, paradoxically, starting to improve the situation caused the stall warning to come on, while doing the wrong thing caused the warning to go away.
Both pilots were trying to debug with information intentionally being hidden from them. (Honestly, the stick should vibrate or something if your inputs are being ignored or counter-commanded by the other pilot. Better yet, mechanically link the controls as in Boeing planes... it's not great that the stronger pilot wins, but at least both know what's going on.) Granted, there was a lot of pilot error in AF447, but there were multiple user interface issues that greatly contributed to the problem.
Edit: Also, as I remember, the start of the incident was that the pitot tubes iced up and the autopilot disengaged itself because it had no idea what to do. It's hard to point to a case where the automation has explicitly given up as a case where we should rely on more automation. Clearly a world where the automation was better would have been better, but just letting the autopilot do its thing wasn't an option. The autopilot disengaged itself.
Not necessarily. They are mechanically linked but there is a breakaway mechanisms designed to be failsafe against one of the sticks jamming. You could have a scenario of them fighting each other so hard the breakaway trips and then only one of them has a working stick, at least until both sticks are aligned, allowing the clutches to engage again.
Loss of pitot tubes only implies loss of air velocity indicator. The attitude indicator, the altimeter and the thrust levers worked fine. I still can't believe they intentionally reduced thrust and pitched up for an extended amount of time, and not only thought this was a good idea, but didn't crosscheck the most fundamental instruments to confirm that the plane was flying level. And then proceeded to ignore stall warnings and stick shaker.
The human error was so severe that I'm not convinced that better alarms could substantially mitigate. At the end of the day, if a pilot forgets how to fly a plane, then their peer (presumably still capable of independent thought) needs to have the presence of mind to take over.
(From Vanity Fair, it sounds like the Air France pilot's union is both extremely powerful, and profoundly hostile to the idea that pilots must actually be competent. Also like opaque layers of both poorly-understood automation and infernally-clever instruments repeatedly got in the way of the pilots doing plausible things to "manually" recover.)