I have never heard that there was a height requirement for servicemen who were present at the Japanese surrender on the USS Missouri. A quick search can't seem to find anything to support that assertion, either. I don't know that we can disprove that claim, and perhaps someone else will have more information that I do (there are several excellent contributors on the sub with great information on the period, and I'm just a hobbyist). But if I were to hear something like that from a friend who had a family member on the Missouri, I would not take it at face value.

To that point, there are dozens (hundreds?) of pictures of the surrender ceremony, and there doesn't appear to be any kind of uniformity with the height of individuals that you can see. In the front row of individuals in this picture, starting from the left and moving to the center of the frame, there are obviously some individuals who are notably taller than others. I still wouldn't say this disproves OP's question, though, because these are high-profile individuals from the Allied militaries. I couldn't name them all, but the one with a garrison cap and his head tilted to the right is 4-star Admiral William "Bull" Halsey of the U.S. Navy. There were 9 Allied countries that signed the Instrument of Surrender, and those individuals stepped forward from behind the table, not at that row to the left in the above picture. From this angle you can see the different uniforms of different countries represented. These individuals in close proximity to the ceremony itself wouldn't have been random officers; you would have had to be someone of significance to be there. And you wouldn't tell Admiral Halsey, or a high-ranking officer from an Allied nation, that he had to stand back because he wasn't tall enough. You could maybe suggest that common sailors who weren't VIPs had to be of a certain height, but given the sheer number of them crammed everywhere for the ceremony, sitting on top of the gun turrets and stacked in rows several ranks deep, it would seem unlikely to me.

However, that doesn't mean that your questions are entirely off-base.

It is notable that the vast majority of American sailors and service members on the Missouri are wearing their service khakis, which would have been the common uniform for a day's work at sea. The Navy had many uniforms which would have been more formal, but the uniform of the day was for khakis. I've never seen a thorough explanation for this; the most common version of the story seems to be that General Douglas MacArthur (who was Supreme Allied Commander in the Pacific) simply retorted that "We fought them in our khaki uniforms, and we’ll accept their surrender in our khaki uniforms." MacArthur, as much as any general in history, was cognizant of his public image. It could have only been a conscious decision that led to this. Stuart Murray, at the time the Captain of the USS Missouri, mentions it briefly in this recollection but there's no specific reason why. Maybe someone else will have more information or be able to provide more context. It's a minor detail to many, but to anyone familiar with the military, it's striking to see the Japanese delegation in their dress uniforms and formal business attire contrasted with the American khaki uniform. It's the rough equivalent of you hosting a business meeting in khakis and a polo, or business casual, when your guests arrived in three-piece suits.

I'd also point your attention to the list of Allied ships that were present at the surrender ceremony. Despite the overwhelming importance of aircraft carriers during the war, there's not a single fleet carrier on hand that day. USS Enterprise (CV-6), perhaps the most celebrated ship of the war, had been on the American West Coast when the atomic bombs were dropped, but almost surely could have raced across the Pacific and been present. More than a dozen Essex-class carriers had been churned out during the war, and plenty of them were nearby as well. But not one of them proceeded into Tokyo Bay. This seems to have been done for at least a couple of reasons.

First, there was a massive flyover conducted by the US Navy/Marine Corps and the US Army Air Forces immediately after the surrender document was signed. Aircraft carriers wouldn't be able to launch their planes while at anchor, so they would have had to be at sea. Second, several accounts also report that there were security concerns. Despite the fact that Japan had ceased fighting in August and the surrender ceremony was a formality, there seem to have been many people who believed there was a nonzero chance of an attack, either ordered by a deceitful Japanese government or fanatical individuals who refused to give up the fight. The fleet would have been vulnerable in Tokyo Bay, and sending in the aircraft carriers was a risk that didn't need to be made. The Missouri's antiaircraft guns on her port side (opposite the surrender) were manned during the ceremony itself. This article has some more information about the flyover, which was quite a feat of logistics and timing. Here's a video as well.

It's also noteworthy that Admiral Raymond Spruance was not present at the surrender ceremony. Spruance had won the American victories at Midway and the Philippine Sea, smashing the Japanese fleet in two decisive engagements. Admiral Chester Nimitz, the US Navy's commander in the Pacific, considered Spruance to be his best commander (he was scheduled to be in charge of the naval forces in a planned invasion of Japan later that year), as well as a good friend. Spruance was invited to the surrender by MacArthur and would have rated a front-row seat at the surrender ceremony but Nimitz ordered him to stay away. Given Nimitz's relationship with Spruance, the most plausible explanation for this seems to be that Spruance was being kept away in case of an attack on the Allied commanders on the Missouri. Someone would have to be around to command the fleet if the worst happened.

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