You're asking an interesting question that I think gets into the constantly evolving historiography of WWII, particularly in regards to the role that America and American G.I's played. First of all, I'm not exactly sure what you mean by chaotic, but you're definitely getting at a trend in military historiography that is becoming increasingly looked at by researchers.

Adam Tooze in "D-Day a New Kind of War" argues that there is tension in the 1980s and onwards between revisionist histories of the D-Day landings, by extension the European Theatre, and the way the war was actually fought. During the landings, only about 14% were infantrymen and another 6% were tank crews. So you are absolutely correct to identify that what won us the war was organizational structure and overwhelming modern firepower, it was indeed dubbed "a rich man's war." It was predominantly fought and won by air strikes, cables, signallers, forward observers, and, most infamously, 'strategic' bombing, which basically meant obliterating entire German and Japanese cities. Where then do these ideas of America being 'chaotic' come from?

Tooze argues that despite the revisionist histories making the case for an impersonal air/artillery war, there were also numerous first-hand accounts of military histories being written that take "us close to the action and the hearts and minds of the men who fought," with a sharp focus on the realities of combat rather than overall strategy or logistics. These were most pronounced in Antony Beevor's D-Day and Allport's Browned Off. These books indeed get into the nitty and gritty of fighting in its abhorrent totality, and definitely could be described as 'chaotic.' And it is these "memoirs and reminiscences" that dominate the historical narrative. I mean, think about it for yourself, would you rather read a book about logistics, grand strategy, and air war, or a book that has the adrenalized heart-pumping action of hand-to-hand combat?

There is another author Elizabeth Samet, a literature professor at West Point, who published a book recently called Looking for the Good War which I think answers the question you are posing here today. She does a survey of multi-media literature surrounding WWII from right after the war in the late 40s and 50s, all the way to more modern times in the early 2000s, and traces how the conception of the American GI in public memory has basically morphed along historiographical lines. One of her interesting findings is that the returning GI in the 1945s had a very mixed reception--in movies, they were portrayed as anti-heroes and featured mainly in Noirs or Westerns as troubled souls who found a way to use their military experience through jobs such as being a Sheriff, or Detective. Part of it is that right after the war ended, America still did not have a firm consensus on why we fought, and why we sent so many men to die, particularly in the Western theatre. We have to remember that the Holocaust was only discovered by American soldiers in late in to the war, in 1944 and 45. It wasn't until much later that holocaust remembrance became common knowledge in America, and the evil of the Nazi regime became widely known (Hollywood was famously pro-German until late into the 30s because they were scared of losing an audience, for example).

So what happens is that in the 1990s we began celebrating the anniversary of D-Day with presidential commemoration, and veteran remembrances among others became a thing. This coincides with films like Saving Private Ryan, and authors like Stephen Ambrose, who fall into the same category of Beevor and Allport--these are exciting narratives told from a triumphalist, heroic first-person perspective that gets into the horrors and chaos of war, but also belies the reality that 80% of the war was fought as an impersonal and modern affair. It is around this time that WWII increasingly comes to be seen as a black-and-white struggle between good-versus-evil, and the American GI becomes apotheosized in collective memory as a figure of good, a liberator of France. The fact that WWII was a reactionary war to Pearl Harbor gets washed away in the literature, and the American GI is seen as someone who went overseas for ideological reasons, to liberate the world from Axis tyranny, despite that most soldiers had very little idea why they were in Okinawa or Normandy.

And the question of why these stories stick with the public more than the academic revisionist histories that give us an 'accurate' understanding of how war is fought has partly to do with the history of the 20th century. This is when America becomes an interventionist global power, and begins waging wars overseas for a plethora of reasons but which include ideological ones. So popularizing military culture through literature that focuses on the 'excitement' of war, rather than its boring points, while also highlighting the unequivocal good and heroism of the average American soldier is entirely in-line with the foreign policy agenda of mid to late 20th century America.

Moreover, much of the political rhetoric at this time, and the way that WWII is thought about in popular memory, loves to highlight the fact that we won because the American was ideologically superior, because the American soldier had a better cause. If we accept that our victory was won through things like strategic bombing, and really, won because of superior material industry, then that undermines the claim that there is something innately superior about the American way of life.

Think about what kind of ideas are becoming popular in the 1970s: Star Wars in 1977, to which George Lucas attributes its success to Joseph Campbell's Hero with a Thousand Faces. People are becoming increasingly interested in the personal story of the scrappy hero who is reluctantly brought into a pseudo-religious, good versus evil narrative to save the galaxy. Interestingly, Roy Scranton, another academic who analyzes WWII literature, argues that almost every story about WWII veterans can be described under the umbrella archetype of the 'tragic hero,' the hero of humble origins reluctantly drawn into a conflict that is larger than him in which he plays for the good guys. This is eerily reminiscent of the narrative structures that are becoming popularized in the 1980s, around the time when Tooze concurs that experimental first-person narratives about WWII are starting to take off. And if we think about the Star Wars narrative as representative of this archetype, the idea that we are the logistically-responsible and organized, a behemoth of industrial power, rather than the scrappy band of resistance fighters, makes us seem more like the Empire than the Rebels, doesn't it?

I apologize if this is a bit hard to follow because I'm currently working on all this for my thesis, but my point is: you have a number of reasons from narrative archetypes, to Hollywood and literature, to American foreign policy, that has an interest in showcasing individual heroism and the virtues of individual, boots-on-the-ground American soldiers, rather than the stark reality that our country fights wars more like the Empire--an impersonal, behemoth-like corporation that bulldozes people with superior long-range firepower and air support, under the auspices of world-ending nuclear weapons (sound familiar)?

Alternatively, a nice and simplified way to view this whole issue is you can apply Occam's Razor and accept the fact that the exciting first-person war narratives, the 'chaotic' narratives, are simply going to win people's interests over the more boring analysis of organization and logistical strength. Over time, as the former ideas win out over the latter on the grand scale they entrench themselves in national and collective memories, and slowly these stories become increasingly taken for granted as our history--this is the complex relationship between myth, narratives, and history, and the infinite tensions that abound between them.

But anyways, your question was a perceptive one and I'm glad that you have recognized this disconnect between the stories you are told and shown, and the actual histories that are being taught.

Edit: Thank you all for the awards and for the kind words and support. I haphazardly wrote this as an addendum to the on-going discussion and did not expect to spur this kind of feedback or debate, but I'm glad for it, and appreciate your support and interest in my research topic.

Accordingly, I want to clarify some statements in light of the much-appreciated criticism and following discussion that has taken place in the comments. A lot of people are asking about soldier motivation and my statement that American soldiers had "no idea" why they were fighting. I will admit this is a bit overstated. There are comment threads below where this is discussed more in-depth in a dialogue that will help contextualize it better.

My point is not that the soldiers had no clear why they were fighting, but they tended to be for reasons that had to do with revenge and groupthink than the ideological or heroic reasons purported later. Americans in politics and everyday conversation love to point out the fact that our soldiers died to liberate the world from tyranny in WWII, point to France, for example. I have heard this parroted by intelligent people at an IR think tank I intern at.

All of this, however, are mistaken sentiments that have sprouted from the historiography of the war putting a focus on the heroism of individual soldiers. Most soldiers had little idea how had bad Nazism was during the war, and were in the pacific theatre for mainly reasons of revenge, coupled by racism that was common to the time. Very few soldiers had an eye for the larger ideological struggle or stakes of the war. And what was meant by the phrase they had 'no idea' why they were fighting is a reference to how soldier motivations further devolve once the dire straits of combat hits.

The answer is that the sources are likely* dubious, as described by u/MaesterBarth:

https://www.reddit.com/r/AskHistorians/comments/58a47j/are_these_quotes_about_americans_disregarding/

There's a good cultural/historiographical answer given in this thread so I thought I'd add in an answer that leans more towards the military history side of things. I'd argue that this "reputation" you describe largely stems from the doctrinal differences between Allied forces during WWII. To pull from Hsieh and Murray's A Savage War the largest innovations that the Americans gleaned from the American Civil War were that of the importance of industrial capacity, logistics, and independent command and control among officers. These last two factors were the primary difference in doctrinal evolution between the Americans and their Allied counterparts. To vastly oversimplify the argument made by Hsieh and Murray, the geographical scope of war in North America created a military doctrine where fronts were so large that independent strategic capability became much more important than in Europe, where independence was important but signals/communication and logistics were never spread so thin as to require near absolute independence of officers during campaign.

To lean on my own research concerning Canadian military history, this requirement for high levels of independence due to geography was part of the reason the Canadians were given their "stormtrooper" or "shock troop" status in WWI. Canadian officers were doctrinally unorthodox in a way markedly similar to the Americans: they favoured doctrine that placed far more responsibility and capability on/to the NCOs and lower COs than their British counterparts. Despite doctrinal evolution by the British, this difference between Canadian and British doctrine still existed through WWII.

Now, the reason I brought up the Canadians as an example was because the Americans were far more evolved than their Canadian counterparts in terms of a robust doctrine that allowed for devolved strategic thinking. If the Canadians were considered "different" or unorthodox in doctrinal outlook then the Americans would have seemed utterly "chaotic". Which brings me to my main point -- American doctrine was far more capable and adaptable at the Brigade or Platoon level whereas British and Soviet doctrine was highly Division/Army focused.

Ironically, I would contend that the logistical skill and organization you cite is actually a large reason in why other Allied forces would have seen the Americans as "chaotic". To borrow an argument from Citinio's Beyond Fire and Movement: Command, Control and Information in the German Blitzkrieg, the German "Blitzkrieg" was largely a phenomenon driven by greater signals capabilities among the Germans which allowed for officers to seize the initiative. The Americans, with the best signals and logistics capabilities, were therefore even better poised to capitalize on the pre-existing doctrine that placed more focus on allowing for devolved strategic thinking.

Effectively, I would argue that the "chaotic" nature ascribed to the Americans was not due to any actual chaos, it was moreso a perception of their doctrine being chaotic when compared to the doctrines of other Allied forces. To their Allied counterparts what was merely allowing Tactical and Strategic adaptability likely seemed akin to improvisation at times. So, in essence, I would argue that the reputation had nothing to do with any actual "chaos" but rather due to a radically different school of doctrinal thought being introduced to Europeans who had a far different, more rigid, strategic doctrine.