You don't need battleships to sink carrier. Japan's very capable heavy cruisers were more than adequate. Yamamoto doesn't know that the US is reading his messages so he should not be basing his decisions on not scaring the Americans.
If the Americans were willing to abandon Midway, Midway was the wrong target
Yes, I am sure he would have done something completely different if he had known they were reading his messages. After Midway, he had to start to suspect...hmmm, American carriers showed up at Coral Sea, and a month later they are there, waiting for us, gotten past our sub picket lines, over 1000 miles north of the Coral Sea.
So yes, he doesn't know they are reading his signals, 100%. In fact, he assumes they are not and are only going on recon intel and possibly radio traffic, which is why the IJN observed radio silence. THEREFORE, Yamamoto keeps his main body back, so they cannot be spotted by PBYs from Midway and reported. Remember, the plan was the Japanese HITTING Midway draws the USN out to fight, after the initial strikes, the plan was never predicated on the USN already being there. Again, think about what was going on, what the plan was, not what we know 70+ years later. Obviously, the Japanese are not completely foolhardy and searched for enemy ships, just in case.
I think if the US intel says the Japanese are fielding NINE carriers, 7 of them being Fleet carriers, 10 battleships, 15 cruisers and 50 destroyers, yes, 100% the USN stays home with their 3 carriers, 8 cruisers and 15 DDs. As it was, 4 vs 3 and they KNEW the odds, they were still governed by not risking their carriers without a good chance of heavily punishing the Japanese carriers in exchange....what did Nimitz call it, calculated risk? 3:1 odds in carriers, your ONLY carriers in the Pacific at that exact moment, and hell yeah they leave Midway to its fate. If they lose those 3 carriers, they have Saratoga and if they are desperate, Ranger, until they can get the Wasp to the Pacific. Then they have to wait until Essex carriers start rolling out in early 1943. Even then, they are still outnumbered and will be reduced to raids again for the rest of 1942.
Would the US have showed up if they knew the Japanese were going to have all 6 (i.e. Zui & Shokaku) big carriers? Maybe, but those are still long odds, even with the element of surprise. Force multiplication says 2 carriers are 4x more powerful than 1 carrier, or 4 carriers are 4x more powerful than 2 carriers...the principle is something to that effect, to basically say 2:1 odds is not 2x more powerful than your force, but actually at least 4x more powerful. In other words, the ratio of numbers was not a linear relationship to the power they could exert.
Name me ANY island base the Japanese could attack that the Americans would not abandon in the face of overwhelming odds? The Americans didn't believe in suicide missions (though you could almost say the Doolittle Raid was one), and going against 9 carriers with 3 is suicide. There comes a point where you say nothing is worth throwing away those 3 carriers, certainly not a rinky-dink atoll that is largely a glorified sub base and forward base for advance warning. We'll wait until a few more of the Essex carriers being built are off the slipways, and we get the Wasp and Saratoga back, then we'll start our offensive a little farther back and the war will last another year.
Midway was, what 1100 miles, from Hawaii? From the US perspective, who cares? The B-17 can't bomb Hawaii from Midway and get back. The G4M cannot either. Maybe the US doesn't know the G4M can't reach Hawaii, but I think it's a safe guess if a B-17 can't, probably their G4M can't make it. The Japanese cannot possibly support that garrison on Midway, long term. The US could retake that island any time they wanted to, really, unless the Japanese commit serious naval assets to hang around Midway pretty much constantly. Its twice as far Japan to Midway, as it is Pearl Harbor to Midway, almost exactly. The US subs blockade Midway and choke it out pretty quickly.
