CFS is a very different catagory to the fatigue that pilots experience. I agree with you that a lot of what pilots experience is tiredness. The problem with fatigue as it applies to pilots is you are not allowed to anticipate that a duty will be fatiguing even if you know from experience that it will be. So you start a duty tired but at the other end (e.g. BOC over multiple days you
will start showing signs of
- difficulties with memory and concentration
- brain fog (feeling like you're in a mental fog)
- visual disturbances (sensitivity to light, blurring, eye pain)
These are the symptoms of fatigue that controlled rest is supposed to alleviate.
Whether the AF447 pilots had this and it had a
major impact on the sequence of events is unlikely IMHO. As has been mentioned, holding the side stick back despite the warnings has more to do with training and deskilling of pilots than fatigue issues.