Why bother? Back to pilot training. We can also do that. We SHOULD be trained to do it (some are).
But what are the limits of what a pilot can do? Set the pitch and adjust the power, OK. Is your average (or even above average) pilot going to be able to factor in issues such as aircraft weight, CofG, bleed and generator load to name a few and select the right values? Will the pilot have any sort of spatial awareness of what is going on with the aircraft? There was a case when a jet took off with the static ports taped up - somehow setting power/pitch didn't ensure a good outcome in that case.
Computers can tackle problems such as these. There are millions of flight hours worth of data available covering thousands of parameters of an aircraft such as the A330. I can imagine that by processing this data it would be possible to develop a probabilistic model of the actual dynamics of the aircraft. Computer processing power is available to analyse the actual flight parameters against such a reference database real-time and (a) identify any discrepancies, (b) extrapolate to a high degree of certainty any missing parameters. The real challenge will be to get such solutions certified.
The pitot-static system relies on a duplication of the same devices to achieve redundancy. This approach was far too simplistic for the computers - not only are they multiplied - but they are in fact totally different computers. If we expose 3 identical probes mounted more or less on the same place to the same conditions we are far more likely to encounter multiple failures then if we have different devices. Why were not the same criteria as applied to the fbw computers applied to the air-data system?