Imperialism in East Asia was quite a different beast from, say the Scramble for Africa. Now, bearing in mind that actually establishing control of African territory was far harder than is generally thought, on that continent you at least saw European countries divide up the map and allocate huge areas of territory to different empires at a stroke.
You never saw any similar process in East Asia.
It took the British 150 years to become the hegemon of India, and another hundred to complete the conquest of the subcontinent. Even then, huge parts of that territory were still under autonomous native states.
China endured a century of humiliations during which it still retained the vast majority of its territory, and in fact saw European empires intercede in 1895 to ensure that their Japanese rival didn't demand too much during the peace settlement.
France took decades to secure Indochina. The Netherlands were still fighting colonial wars in Indonesia into the twentieth century. And so on, and so forth.
The idea that America could unilaterally seize the whole of Japan at a stroke is simply without precedent.
Leaving aside the fact that you still haven't established why they would want to do so- there is absolutely nothing they can get from an occupied Japan that they can't get from a Japan that is open to trade- they would not be in any position to launch an invasion until they'd secured the Philippines, at which point Japan itself was far too powerful for any attack to succeed.
But my broader point is that even if they wanted to attack, and even if they could attack, doing so would be incredibly destabilizing to the international order in Asia.
The British Empire would be absolutely furious, seeing as keeping the Japanese and Chinese markets open to all was their key policy in the region- in our timeline we associate the 'open door' with America, but do not underestimate the laissez-faire City of London's power here. An American Japan would also encourage territorial expansion into Manchuria, Mongolia and North-West China by the Russians who could point to an American precedent- which would make it even more important for the British to stop the American annexation.
Of course, the Russians would at the same time oppose the Americans moving in even as they enjoyed it providing cover for themselves- because they don't want a powerful, industrialised empire on their eastern flank.
The French had occasional designs on Korea, which will be threatened. So they'll oppose.
So, for that matter, will the Qing- who, weak as we generally see them to be, were at the time regarded as a formidable power who had to be dealt with carefully (if patronizingly.)
If you want America to rule Japan, I give you our timeline from 1945 to the treaty of San Francisco.
Anything earlier is ridiculous.