A couple of things that haven't been mentioned much:
The response a member of staff receives when reporting fatigue/unfitness will presumably depend a lot on their previous absence record. If it's someone who never goes off sick or is late and is consistently reliable, then presumably it'll be taken seriously, however if it's one of the depot skivers (and I'm sure every depot has some), it's more likely to be treated with skepticism.
Secondly, I feel it's a bit strange that the default position is that we rotate between lates and earlies every week, or in some cases every two weeks. The sleep pattern changes, especially lates to earlies due to the human body having a 25-26 hour body clock, can be very challenging. I'd have thought it more logical to split each link into earlies and lates sub-links and if there are vacancies in both, ask for preference when entering the link, otherwise a position is filled with a waiting list for transfers. Once I'm productive at my current depot, I'm planning on putting the word out to try and get a permanent swap for me to work lates.