Several factors all played their roles, which in the end contributed towards the IJN choosing the path of least resistance and sailing with just the 1st and 2nd CARDIV's. In fact quite the opposite happened! Several of the survivors of the 5th CARDIV's air crews were held to preexisting orders which sent them to other units, including elsewhere in the Kido Butai, which helped make up some of the attrition those units had suffered in the previous 6 months. Meaning of course the bombed out Shokaku and relatively fine Zuikaku were left behind when their cousins left.

Theoretically of course there could have been time to assemble at least something like the proper number of aircraft and crews. Zuikaku already had all the survivors of both aboard when she reached Kure on 21 MAY, and the KB would not sail(a day later than planned) until the 27th. Between aircraft at hand, and shore based units and operational training formations the aircraft existed within range.

So why not? IT comes down to several mutually reinforcing factors of doctrine, preferences, and intelligence of enemy forces.

IJN doctrine of 1941/42 was not as completely rigid as might sometimes be stated, but certainly preferred to deal with whole, complete, organic units. You couldn't, say, just assign the VF squadron from a carrier to a land base or vice versa because both were component parts of larger formations. While this is really just in the end administrative hand waving, it was both a reflection and reflected on how the IJN operated, which contributed to the decision not to form a scratch air group.

On the individual air crew, and larger squadron level the IJN figured it could take anywhere up to a year of training and operational practice before peak efficiency was reached. That time would be spent in training as flights and larger formations to make reacting and coordination almost instinctive.

So less than a week would have been hilariously short for even familiarizing the new squadrons with each other, even if Zuikaku had spent every one of those days underway conducting flight ops, or they had been going non stop from an airstrip ashore. Neither of which would have been possible.

So if a force that couldn't come anywhere near to IJN expectations of mature, ready, combat units was all that might haveb been assembled then we should ask under what circumstances the KB air staff might have made the breakthrough and thrown something together. The answer is of course in circumstances where the 5th flight deck might have been expected to be the difference between victory and defeat.

And the entire leadup to Midway is a demonstration, that aside from personal worry, the official line is nothing both assuredness of victory. Planning is rushed and convoluted, war gaming is pro forma and leads to little meaningful input. Additionally IJN intel is working off the assumption that both carriers present at Coral Sea were sunk by the 5th CARDIV amateurs, meaning the USN was thought to have just 2 carriers left. And that the line of I-Boats to position themselves between Midway and Hawaii would alert the fleet to their arrival in the area allowing the Kido Butai to concentrate against them once Midway was pacified.

'Victory Disease' is something of an overblown critique I find often, but we most admit that a remarkably cavalier, unconcerned attitude was present in many key leaders from Yamamoto on down. The plan left very little room for agency on the part of the USN not playing their part according to script, and the growing competence displayed at Coral Sea could be waved away as against the JV team of Japanese carrier aviation.

In that environment its easy to see why there was no rush to go against the grain and all normalcy and try to get something together for Zuikaku.

We can of course greatly contrast this with the experience of Yorktown and her air group. Battered but still able to conduct flight ops when she returned from the South Pacific she was quickly taken into dry dock. Fletcher meets with Nimitz and Spruance in a hurried conference about the imminent battle while TF-16 sorties. Yorktown though needs her own replacement aircraft, especially her fighter squadron. Luckily just such help exited, Jimmy Thach had been slowly rebuilding VF-3 ashore after they had been left behind by Lexington and his squadron raided for pilots and aircraft. So he takes his boys aboard and absorbs the remains of Yorktown's VF-5. In the few days they have he attempts some training flights, but never has enough time to work through the new 'Beam Defense' tactic he had worked out. Thus only his immediate wingmen use it at Midway, but it proves immediately effective. From then on the 'Thach Weave' becomes a standard part of the tactical toolbox for USN fighter pilots.

Youll always see Shattered Sword suggested work on the IJN at Midway, and that still holds true!

But for the more nitty gritty of the USN and IJN aviation through the first year of the war, including pre war doctrine, training, and operational realities I would also suggest The First Team and The First team at Guadalcanal by John Lundstrom. He actually began uncovering a lot of the new to the West revisions to the narrative that would be expanded upon by Parshall and Tully in Shattered Sword way back in the 80's.