That's not my point. I don't see where the fly by wire system specifically caused the problem in this particular accident. Maybe there was insufficient cockpit indication that the aircraft switched to alternate law? Maybe the pilots were insufficiently trained on the scenario of icing leading to auto pilot disengagement? Maybe the pitot tube design was problematic and led to excessive ice buildup? Maybe the pilot was having a psychological problem, or was too fatigued? Etc

I see. Hypothetically, if there was no fly-by-wire system on that airplane, both pilots' input controls would be coupled to each other, eliminating the possibility of confusion as to what inputs are being made. In fact, all potential UX issues in regards to communicating the current input state to the pilots would be designed away: averaging the inputs, hiding the input of one pilot from the other, the possibility of dual input.

These aren't necessary characteristics of a fly-by-wire system, but its mere existence opens up the design space for them to exist.

Of course, I'm not arguing for removing the fly-by-wire system altogether ;)

However, whenever such fundamental paradigms are changed, great care must be taken to understand exactly how the new one differs from the old one.

In this case, the old direct input system afforded perfect communication of its state by default, but the new fly-by-wire system didn't. Care should have been taken to fully replicate the old behavior in the new system.