On the contrary - computers are much better at mathematics, trigonometry and other complex calculations at high speed, and they relieve the pilot of a lot of workload. Airbus Systems have all been well tested with multiple redundancies built in. Something else happened that made both automatic and manual control impossible.
Much speculation concerns the ACARS messages - but if there was a catastrophic failure some of the more informative fault reports may not have gotten through to the COM link or they may have been queued for transmission but never made it. We shouldn't assume that the faults transmitted were the principal faults that occurred. For instance if another unreported fault disrupted power to the pitot heating, then the latter problem would be a symptom and not a cause.