Is their no backup system available in the event of pitot tube failure?
Well, yes there is. The other 2 pitot tubes. Trouble is when there is a common problem affecting mroe than 1
Pilot error is surely a factor in this case, but a more significant factor is the failure of aircraft manufacturer's to recognise that automated systems should be designed as an adjunct to a pilots flying skill and training, and not as a substitute for it.
This situation began because the AP disconnected, and the situation degraded because the pilots did not understand what was going on.
Your 2 statements do not quite add up
The AP disconnected precisely because '
that automated systems should be designed as an adjunct to a pilots flying skill and training' occurred - the AP was not able to determine what was happening to a sufficient degree - the system designers / regulators decided that was a point to hand it back to the crew.
Now as you say '
and the situation degraded because the pilots did not understand what was going on' and that is an issue for training / skill / practice. Now I fly "made in Tolouse" products for a major European airline, LHS for nearly 10 years. I do not recall one sim training session where I was "persuaded" to be distracted / looked down / pretend dozed off, and then given the aircraft in an unusual attitude, with some systems / insts failed, and told to resolve it *. I do recall being given some very gentle stall recoveries to perform, precisely, with a detailed brief in the minutes before "to address the AF issue" (all systems working except in Altn law)
* The sort of UP recovery every RAF student pilot started doing at ~25hrs and in every IF training trip / test thereafter.