Whilst it's understandable to proclaim that Montage Theory doesn't receive the amount of 'attention' it deserves from Hollywood, this is closer to the concept of Montage Theory (MT) not receiving overt 'credit' when it does appear; largely due to its indelible influence.
Montage theory marked the beginning of a filmic language; the idea that film is something to be edited in order to create meaning, and that composition is used to tell a story as much as what it is you're shooting with the camera. Prior to Montage theory, films were produced almost in the style of plays; with a stage on which actions are performed, and the camera substituted for the position of an audience.
Imagine every film being staged and produced in the style of a US sitcom, and then someone coming along and introducing camera angles, crane shots, pulleys etc... It was an epochal shift in cinema.
Elements of montage theory still exists and can be evidenced across every film making style in the world, such is the impact of the Soviet Masters; they're just so common, so well adopted into the grammar of film making that we no longer flag them up as important. Typically, shots that don't adhere to elements of Soviet Montage are considered jarring or obtuse, such is our familiarity and preference for certain elements of continuity produced by the Soviet Masters; typified by three figureheads of film making whose contribution to cinema can not be diminished.
The general grammar of the shot has developed to embrace the styles of these three film makers, so we don't notice when they're being deployed. For example...
Sometimes referred to as 'Shot/Reverse Shot' This is a type of shot sequencing that is used in almost every TV/Movie production you could name: Lev Kuleshov noticed that if you juxtapose images in sequence, the human mind will naturally compose them into a linear, formal narrative. What this means is that we, as observers, will naturally correlate the two images to be in reaction to each other. We will infer a connection between the imagery, and in the case of human reactions (below) will assume that the facial expression depicted is in reaction to the previous shot...
It can be difficult to grasp what is so special about this style of shot, because it's so well used, but the significance is that Kuleshov invented this style of continuity.
Hitchcock, in the famous "Definition of Happiness" interview, also explains in detail many types of editing. The final form, which he calls "pure editing", is explained visually using the Kuleshov effect. In the first version of the example, Hitchcock is squinting, and the audience sees footage of a woman with a baby. The screen then returns to Hitchcock's face, now smiling. In effect, he is a kind old man. In the second example, the woman and baby are replaced with a woman in a bikini, to which Hitchcock exclaims, "Now look, he has become the dirty old man."
Before he demonstrated an edit (or montage) sequence which broke the formalities of existing cinema, continuity was achieved through incredibly condescending shots that held the audience' hand through events; they were simply not trusted to understand that two separate shots were connected, as most cinema was constructed through wide angles on a one shot-stage, enveloping the scene entirely as opposed to building it through separate shots...
- The Basic Film Grammar of Dziga Vertov
A claim could be made that Dziga Vertov (which translates to 'Spinning Top' in recognition of his then radical filmic style: real name David Abelevich Kaufman) invented many of the elements of continuity that we take for granted in cinema today.
It has been greatly disputed how many of these he actually invented, but the reality of his importance is within his ability to combine them together into a coherent, emotive form within his seminal film Man with the Movie Camera...
Amongst other elements, he is said to have 'invented' (or been the first to successfully deploy);
footage played backwards
stop motion animations
As you can see, that's quite a list, and none of those claims are unfounded in the least. Man with a Movie Camera is often recognized as the most important film of all time, in due respect to how incredibly innovative and pioneering its techniques were, and its ultimate contribution to modern cinema...
Now we're able to see why MT is so important, and understand that it is still incredibly prevalent in cinema, we must understand why it is relatively unspoken of.
There are many socio-political factors which contributed massively to MT theory being 'overlooked' for so long, and it's fair to say for the first part of the 20th Century the contributions of the Soviet Masters was deliberately obscured. That isn't to say that these techniques weren't used and deployed; it's just that the lineage of their construction was often ascribed to other, less politically volatile and more populist 'inventors'... Chief amongst these being Thomas Edison.
Despite a wave of American sentiment towards this historical figure, anyone that undertakes a study of his legacy will quickly realize that Edison was an utter, utter Ass-hat. Many researchers have taken lengths to explain how Edison stole most of his greatest inventions, but his accidental contributions to cinema are often overlooked...
For example, Edison accidentally invented Hollywood.
Edison, through a strategy of Bullying, intimidation and patent theft managed to lock down the US cinema market in the early years of the 20th Century; it was impossible to to make a movie without using Edison's equipment (he'd patented them all, or legally wrangled the patents away from those who actually held them) so everything went through his company.
The Jewish Film-makers of New York, tired of constantly having their earnings diminished and being censored by Edison, upped sticks and moved west until they were clear of the stranglehold of Edison's malevolently suffocating Motion Picture Patents Company. They found a lush, bountiful and incredibly cinematic landscape within the Cahuenga Valley with incredible natural light that allowed them to create beautiful external shots: they named this new film-making mecca 'Hollywood', and the rest is history.
What does all this have to do with MT I hear you ask?
Well, Edison hated anything that either deprived him of money/prestige or disagreed with his vision (as evidenced by the lengths the Hollywood Diaspora took to escape him), and would actively pursue campaigns to discredit anything that disagreed with what he considered to be 'Cinema'.
Edison's cinematic style was incredibly formal, standardized and simplistic. All films were produced inside a 'Black Mariah' (Below), meaning as far as Edison was concerned you could only make a film using his equipment, and his sets...
So as far as he was concerned, anything that didn't look like his style of cinema wasn't cinema, and as such needed to be discredited so as to neutralize it as a threat to his authority. By looking at two clips, below, we can see the gulf of difference between what Edison (and through campaigns of propaganda, the American public) considered cinema and what the Russian Masters considered innovative cinema:
Whilst it must be noted that MWTMC came much, much later than Edison's work, it represents the epitome of a different style of film-making that Edison took exception to (at the time, Edison aimed much of his aggression against the Lumiere Brothers of Paris, but his methodology was to ingrain the notion of Foreign=Inferior, a policy of which the Russian masters felt the brunt of in the States).
Edison laid the groundwork for a swell of public opinion that sought to diminish the impact of anything non-home grown, and by the 1920's (with Hollywood firmly established as one of the countries biggest and most profitable industries), credit would rather be applied to their own talents.
With Europe and Russia being ravaged by 2 World Wars in relatively quick succession, America was the film industry that was able to pick up the slack and production from the cessation of cinema in Europe, and they readily adopted the style of the Soviet Masters within their work. The reason they weren't all heaping praise onto those who deserved the credit for the techniques?
...A huge swell of Anti-Russian sentiment within the states, typified by the McCarthy trials and the HUAAC.
With communism providing a genuine threat to 'American Values', anyone who would seek to promote or endorse anything that came out of Russia would be labelled as a 'Red', and undergo black-listing, deportment and imprisonment. It was a dangerous thing to draw attention to how much of cinema, that most American of entertainments, was massively indebted to Russians, so it's understandable why this wasn't something widely discussed within the States.
It didn't help that directors like Eisenstein were inherently political, and socialists themselves...
His film Strike! is still regarded as one of the most influential political films of all time, and was a veritable rallying point for the socialist movement. It was a dangerous film to America's fordist consumerism, and as such he was automatically black-listed. His films also employed artistic derivations of Soviet Art in its composition, with the Battle-ship Potemkin using jump-cuts and overlays to achieve this mimicry incredibly...
Again, MT still being used by Hollywood, just not being drawn attention to.
By the end of the wars that had reduced European/Soviet cinema to state-sponsored propaganda, and the Paranoia that came immediately afterwards, MT had been deployed in cinema for half a century.
People were free to discuss it without recrimination, and film scholars did, but for most of the population of movie-goers there was simply no need to discuss such a thing. It was by this point the natural style of cinema, and if anything was incredibly basic. Film-making had evolved beyond an interest in basic continuity and shot composition, and areas of interest had moved on to more innovative techniques... it had lost it's sensationalism, but never its relevance.
This question was initially close-voted due to users unfamiliarity with Montage Theory as a concept, which I think demonstrates conclusively how successful the campaign of disaccreditation formed against non-domestic US cinema by Edison was: it holds true to this day. MT provided some, if not all, of the major types of standard continuity used today: 100 years later, we've still not found a better way to do these things than the Russian Masters.
The fact that not only are film-fans unaware of what MT's contribution is, but also (as close voters demonstrated) have never ever heard of it, is pretty staggering: given its contribution and importance.