Here's where I am starting from:
Aleutians, Battle of Dutch Harbor - June 3–4, 1942. 2 smaller aircraft carriers.
Main Midway battle. June 4-7. 4 big carriers, with 2 smaller that weren't right there. US puts 3 carriers.
Leaving alone why the 6 carriers got split into 4 and 2 at Midway, why didn't the Japanese concentrate all their forces?
Now, in wars, concentration of forces is generally considered a good thing. But there are valid reasons for splitting up an attacking force: a diversion to lure defenders elsewhere, a simultaneous attack to force the defenders to split up their forces and finally increased opportunity for flanking the enemy when your forces are not too widely separated.
The Aleutians sideshow fit badly on all those counts. Coming so soon before Midway, the US Navy wasn't going to send off its carriers there in time to strip them from Midway. And conversely, being so far away, each US force was acting independently anyway.
Now, Midway is thought of as a great US victory. And it was. But it might easily have been a disaster. The first attacking US torpedo planes had been entirely destroyed until the dive bombers arrived just when the Zero's CAP was occupied with the lower level torpedo bombers. And the Japanese still managed to sink 1 carrier. At this time of the war, the Zero was still dominant against Wildcats and Buffalos and they still had their very best pilots around.
Having the 2 smaller Alaska carriers could easily have made a difference, especially as a big part of carrier engagements was finding the enemy carriers - even a relatively small attack wave could get lucky and put a carrier out of action.
I did watch a Youtube about the Coral Sea battle and, yes, it seems that Japanese Navy loved complex plans with lots of different forces. And, yes, what might seem natural to Westerners raised on Clausewitz and Napoleon - pushing for a decisive battle with all your forces - may not be as appealing to Japanese, especially if someone like Sun Tzu was an influence.
But I still utterly fail to understand why the Aleutians couldn't wait until after Midway. Was that somehow related to Japan's shortage of ship fuel, that they wouldn't have been able to do both?
Edit: I've added why a diversion to Alaska, on the 4th, would be not help and in fact would be disadvantageous to the Japanese, if the USN went for it:
I should have mentioned the cracked codes, but they are not a factor in how Yamamoto reasons about Alaska as a diversion (even if they screw up anything Yamamoto does decide to do).
Think of this as a game of poker. Yamamoto does not know the US sees part of his hand. He can't know the USN will never fall for an Alaska diversion, but he can apply logic to calculate what the effect of the US taking the bait would be.
Let's say he wants to get some part of the US fleet underway towards Alaska so that he has more time to invade Midway without interference from the US Navy.
If it is a diversion, the whole point is that the USN needs to be spun up/prepped for depature and then head out
5000 3700 km away to Alaska. What's that gonna take? 12 hrs? 24 hrs? If it takes the USN 24 hrs to be ready to sail, then after Alaska on the 4th, they are ready to sail on the 5th... just as the IJN is striking Midway. Essentially, Yamamoto is giving the USN a 0 hour response time.
Would you, as a Japanese planner, assume that your enemy would be able to ship in less than 12 hrs, on this level of deployment? Capital ships on a 3700k/4-5days trip that's going to take them to a combat area where there may be no US fuel stations left by the time they get there? Assuming they launch at all - it's a very risky-sounding deployment for uncertain upsides. Because that's the "good reason for doing this" assumption for a June 4th Alaska strike if it is meant as a diversion.
The Royal Navy, as far as I understand, when they heard the Germans were out, took 8 hrs to leave Scapa Flow, their base, on the way to nearby Jutland (BBC Jutland timeline). But the 1916 RN is probably not what the 1942 USN is at this stage. Much less what the 1942 IJN thinks the USN is capable of doing.
Then, once the USN is heading out, since you want to gain time, you need to have them sail further away. If they were going the opposite way, say 180 degrees towards Panama/California, then you'd pretty much win 1 day for each day they went out.
But... PocketEarth, one of my favorite apps on iOS, one I have no affiliation with, says: 3500k @ 351 to Dutch Harbor. 1960k @ 296 to Midway. So the USN is getting closer to Midway as it heads out, for at the very least 2 days then, past that it takes an extra 2 days till they're actually further from Midway to help than without that diversion. All this from whenever they leave Pearl Harbor.
Now, take away "Alaska is a diversion" and replace "And the boss says to do Alaska. Them US Navy guys are pushovers anyway. Same time, so they'll be sleeping again".
Or whatever other reason, just the diversion idea, on the 4th, makes no sense and these pre-computer guys are very smart with numbers.
The cracked codes make it a lot easier for the US Navy to win. But the victory is not a foregone conclusion, look at the actual battle. The level of courage and sacrifice by sailors and pilots of both the IJN and USN is tremendous, but a lot of it boils down to luck and those 2 carriers could have helped the Japanese quite a bit.