With respect to your last paragraph, one of the problems was the way task group operations had not been practiced since the run down of the big deck carriers started. As such it is unlikely that any possible task group commander would have had experience of using fighters as a task group weapon.The best way to regard Sharkey is to break his career into two (and his word processor if possible).
Part 1: Excellent Sea Harrier pilot, leader of his squadron, brave bloke
Part 2: Utterly rubbish historian, prone to inventing stuff as his resentment towards the RAF increased, now a vexatious and incredibly bitter man whose efforts to promote the FAA have, in some respects done it great damage. His penchant for submitting pernicious nonsense to the Defence Select Committee and any journal willing to publish his material in his quest to destroy the RAF, or to at least remove it from anything to do with the maritime arena, is an awful shame. His questioning the courage and competence of Tornado GR1 crews killed in 1991 - despite poorly disguised denials - verges on the contemptible.
As I've said before, I yield to no-one in my admiration for Sharkey Ward, Sea Harrier pilot and leader of 801 NAS; it's his subsequent performance which is deplorable (a view shared by at least two former 1SL...)
The book needs to be read in conjunction with Jerry Pook's Harrier Ground Attack Falklands and Dave Morgan's In Hostile Skies. Pook's book is the product of his resentment at the manner in which Captain Lyn Middleton (mis)handled the Harrier GR3s on Hermes, while displaying an utter contempt for the RAF which, on occasion, could have got people killed. It needs to be read with that bias understood (and that it is - remarkably - toned down from the original manuscript at the behest of the AHB). Morgan's book is more balanced view, although you can see - as in Ward's - that the SHAR and GR3 pilots (and not just Ward, Pook and Moggy Morgan) had growing reservations about Middleton's handling of the air side of things. I would also observe that there is some evidence to suggest that Sharkey's contemporaneous recollections, to be found in the archives, and Sea Harrier Over the Falklands have some er... disparities.
Woodward's Hundred Days is also worth reading, although some of his contemplations about air power are a little off-beam; as he himself admitted, as a submariner, he spent most of his career hiding from aircraft rather than attempting to integrate them in a battle.
Woodward was able to direct ASW activities, and understood the problems our own submarines would face, such as when shadowing the Argentines and understanding the issues with using an SSN to intercept. I am not sure if sixties/seventies technology allowed SSNs to integrate with task groups.
Woodward had also commanded a Type 42 destroyer (HMS Sheffield).