Ever hit the wrong key in emacs and wondered why it was suddenly responding differently? Imagine that happening at 38k feet, at night in a thunderstorm.
My doctoral work was exactly in this field. Mode awareness, transitions awareness and autoflight understanding, especially in rare flight configurations, is a deep problem that needs to be tamed.
More info in my dissertation (never though I'd write that on HN!): http://dspace.mit.edu/handle/1721.1/9172
My opinion is that requiring mode awareness is a big chunk of overhead. It should be eliminated wherever possible.
Removing that restriction allows anything to happen at any time. This is believed to be more complex to model.
Think of modes as a mechanism to prune a decision tree.
Pivot tubes are 'tubes' located away from the body of the airplane for the reason that they get away from the boundary airflow to give accurate airspeed readings. Attempting to 'compensate' for other factors just introduces more uncertainty, which is exactly what you don't want when you're 5 knots above stall.
Let's imagine a plane starting take-off roll. Engines are spinning up to full throttle (99-100% of thrust), but airframe just started to accelerate slowly. Compensating for anything is pretty useless in this case - airflow trough the engines is even higher than during cruise, but airflow around wings is quite minimal.
There are such things in the engines! They're used to feed the data about engine performance to FADECs (http://en.wikipedia.org/wiki/FADEC) and the crew.
But they're totally useless for airspeed calculation! Bear in mind that air flowing trough and around the engine has totally different dynamics than the air passing around the rest of the airframe. Well, that's kind of the point of the engine - to create thrust, isn't it? That's why airspeed, altitude and AoA sensors actually have to be placed further away from the engines - so that they give as accurate picture as possible.
I don't mean using it as a primary source for airspeed data, but backups in case other sources show weird or no data. The data that comes from those sensors already enters the cockpit, so it would make sense to use it.
But yes, I think the conclusion after AF447 investigation is completed will be that some kind of back-up speed indicator is needed beyond pitot tubes.
BTW, I imagine a pitot tube placed on the body of the engine would not need extra heating and would be very unlikely to ice. You can even place it inside the exhaust and compensate the reading for engine flow.
We have to figure out what went wrong, what mistakes the crew made in order to prevent future accidents like this.
And I, coming from a third-world country, take offense at your statement. Pilots here endure very thorough training. One would have to be a lunatic to trust his nephew to a flying computer. The pilot must always know what's going on.
And that brings the main point: people die when the machine surprises its operator. "Smart" planes have become so smart pilots have trouble understanding what they are doing under all that software. And that's assuming the software is not buggy and they didn't got a very unfortunate NullPointException in the worst possible moment.