Perhaps this is missing an important point: it is often the relationships between key individuals that make or break a team.
Look at Duncan Fletcher: lauded for beating the Aussies in 2005 and lambasted for losing in 2006/7. The difference? With Nasser Hussain DF turned a failing team around, with a (apparently drunken) Flintoff, the wheels - or whatever Pedalos run on - came off.
Flower's turnaround of the post KP/Moores debacle shouldn't be forgotten. Clearly he and Strauss worked well together, until the strain of KP got too much for the latter.
This doesn't necessarily mean that Cooky was the sole cause - just that at the time he took over the team was perhaps relieved/shocked at what had happened and facing weakened sides, which changed as the team began to face improving sides (e.g. Lehman era Aussies). I always worried whether Chef had the strength of personality that could keep the side together. Neither he nor Flower are demonstrative characters, with the similarly reticent Gooch on board there was a clear need for more extroverted personalities to lift team spirits - hence the loss of Swann seems to have had a profound effect.
The situated nature of coaching/managing/captaincy tends to be forgotten. It would be an interesting experiment to put a Lehman-like personality in. I take the point that a lot of improvements were introduced under Mickey Arthur or were down to individual mindsets (e.g. Mitch Johnson finally getting his mind & body together). Indeed, this reinforces the situatedness of managing/coaching.