The mechanical back up relies on a working hydraulic system, which is powered by the engines. No electrical system, no engines, no control.
Well it's a long article I linked to, so perhaps you missed this:
"The hydraulic systems will still work for some time if they stop being powered because some power is accumulated in the reservoirs."
The main point is that there are plenty of modern commercial airliners for which it simply is NOT true that "If those computers fail the pilot is completely powerless". I don't claim to know if that is the case with all or even the majority, but I suspect it is.
This sentence, added as a bonus example of an even more extreme case, is the one you disagree with. Note the emphasis I've added on 2 words:
Even total loss of all electrical power AND all computers, which would be much more serious than computers alone, does not instantly leave the pilot without any control at all.
It's not essential to the basic point, because the total loss of all electrical power on a modern commercial aircraft is fantastically unlikely because of redundant power sources. Typically there are at least 3 completely independent and fundamentally different kinds of electrical power sources. Often, one is powered by air pressure from forward movement like a giant pitot tube. Another is simply a big stack of batteries. Unlikely as a total failure of the fly-by-wire system is (there is redundancy in that too), the probability of total loss of all electrical power is almost certainly lower. Nevertheless, if complete loss of electrical power DOES occur, in some, I suspect most, systems there will be a grace period before all hydraulic pressure is lost. Possibly enough, depending on the circumstances.
I'm not trying to "look too good or talk to wise" here. I'm not a pilot. I took the ground school but couldn't afford the lab course past the first lesson. I'm not claiming that flying one of these aircraft with a disabled fly-by-wire system would be a trivial undertaking. My point is that the claim that it is IMPOSSIBLE and that human pilots on commercial passenger aircraft are merely there for public relations is incorrect.
The mechanical back up relies on a working hydraulic system, which is powered by the engines. No electrical system, no engines, no control..
The fly-by-wire system ALSO depends on hydraulics. But neither electrical power nor hydraulics are totally dependent on engines, at least not with all aircraft & I suspect not with any, The famous "miracle on the Hudson" landing was caused by sudden loss of all engines and was NOT simply a case of an uncontrolled falling out of the sky with a pilot having nothing to do. If there had been no pilot, there would have been no survivors.
You clearly appreciate that hydraulic pressure is pretty darned important in these types of aircraft. Total loss of hydraulic pressure is probably more serious than than any of the failure modes mentioned above - indeed, more serious than just about anything short of having a wing fall off. And this has been true a lot longer than fly-by-wire has been around. And yet . . . with the right stuff, always think hard before saying anything is IMPOSSIBLE:
That's the video I couldn't find earlier. I misrembered a couple of details & had trouble finding it, but that's it.
Here is another link on the general subject:
https://www.quora.com/What-would-happen-if-an-Airbus-A320-lost-all-power-in-flight-Would-the-pilots-still-have-control-of-the-plane-because-it’s-flown-by-wire