In the AF447 scenario, the computer decided it did not have reliable air data, so it not only disconnected the autopilot, it dropped into alternate law. Basically, the computer just punted and said "your airplane!" This might seem like reasonable behavior, but one might imagine that handing a degraded airplane to a pilot at the very worst moment is not a satisfactory failure mode, and in the AF447 scenario the outcome was obviously bad.
This seems reasonable, and I still think it is. I don't think Airbus has changed this behavior after this tragedy (but don't hesitate to tell us if they did, as I may have missed the info), so a lot of people have probably considered it reasonable as well. The moment this happened, the plane was NOT in a critical situation whatsoever as far as I remember, so yes this was stressful and pilots got misled somehow, but they would have had ample time to handle this the right way. Turns out that the training on those airliners with a lot of automation don't always have enough simulation sessions for handling this kind of situations, and that's one of the things they improved after the accident: training sessions. The warning indicators are not always very clear either, and this surely could be improved, but at least in this case, they were certainly not lacking as there was a continuous stream of warnings including stall warnings IIRC. The main point as I remember is the pilots were not trusting ANY indication anymore, so obviously they lost all reference and situational awareness.
Again, if some automated system RELIES on some sensor data and this data is DETECTED as not reliable, the system should obviously be disconnected.
That said, if alternate systems that DONT need those sensor data can still be activated to make it safer, of course this could be a good idea to activate them. But keeping on a system that takes some of the controll OFF the hands of the pilots based on unreliable data is a recipe for disaster. That's all I'm saying here, and this is also what has been pointed out and suspected in this Lion Air case by some.
Very interested in reading the final report.