How many Airbus of all kind are flying around the world again? Falling like flies? I don't think so!
Many of these planes are probably not well-maintained and are approaching the age where problems start showing, exactly like any car that isn't maintained properly. If the operator doesn't invest in maintenance, that's not the plane's problem.
Pure "Fly-by-wire" planes are quite new. Even for Airbus. It's only present in newer models, circa 2006 if I'm right. It's been around since ages with military planes. Fighter planes could not be flown by a human unassisted by a computer because they are designed to be unstable and a human could never react fast enough to prevent a crash.
The pure "fly-by-wire" planes are planes where the control commands have no physical contacts with the control surfaces of the wings.
On older planes, the control surfaces are linked to the "stick" and "pedals" by steel cables or hydraulics and can still work to a certain degree if the computers fail.
With a pure "fly-by-wire", the controls are connected to A FEW computers, not just one, who in turn control A FEW, not one servo-motors and actuators. The electrical systems for these flight-critical systems is usually doubled, if not tripled.
Some older planes (almost all line aircrafts) are a mix of "fly-by-wire" and old-style hydraulics/cables systems. The "autopilot" work in parallel with the direct controls, and can always be overpowered by the pilot's physical strength yet, the autopilot can fly and land the plane on it's own. My fun when I travel is to find-out when the pilot land in "automatic" or manually. If possible, I ask him when exiting and I'm usually right!
In true"fly-by-wire" or hybrid systems, there's some mecanisms allowing overpowering in a sense where, if the plane detects a command from the pilot that contredict it's program, the pilot will be given the option to override.
More than often with the newer hybrid or true fly-by-wire", in a case where a perfectly-good airplane crashes, it will be a case where the pilot didn't believe what the airplane was saying or just didn't notice for some odd reason and, knowingly or not, he overpowered the plane's decision. It's sometimes the result of a misunderstanding of the different "modes" used by the autopilot, causing the pilot to try have the airplane do something the autopilot can't do in the selected "mode" and the pilot not noticing what's happening.
If you read the NTSB reports, it's amazing to see how many of the crashes were caused by compounding errore, one on top of another, either caused by the pilot's lack of confidence in the plane or the airline's procedures not allowing the pilot to use his brains and only allow him to use a checklist to resolve problems.
We also have to remember these airplanes are fast so, the time we, sitting on our favorite chair, see as perfectly adequate for troubleshooting a problem is in fact extremely short when you are in an emergency situation. I know because I've been there, in the middle of nowhere, no roads or runways, engine shuddering madly... It took me maybe 2 minutes to realize I had ice in the carburator but these 2 minutes didn't seemed that long... 2 minutes can make the difference between a totally frozen carb and just open enough so the engine generate enough heat to melt the ice.