Or, is the conventional wisdom wrong, and "Akira" really wasn't that important in the development or popularization of anime in the West at all? If not, why not?
Well, first recognize that Akira is an exceptional film even within its own genre. Most animated films in Japan cut a lot of corners, one example being that the mouth animations of characters are done prior to the voice track being recorded, so there is often a discontinuity between the dialogue and the movements of the animated character's mouth. For Akira the animation was done after the dialogue was recorded, leading to much more realistic and natural looking facial motions, especially for particularly expressive dialogue. Another common trick in animation is to only animate a small portion of a scene, relying on a static background (perhaps in linear motion) for the bulk of what's visible. Akira, however, tends to use full character animation, multiple character animation in one scene, animated scenery, and so on.
Then you have the soundtrack, which was created for the film by the musical group Geinoh Yamashirogumi, which is practically an experimental "world music" research institution. This led to a very unique sound for the film, further amplifying the uniqueness of the other qualities of the film's production and contributing greatly to the overall production quality and storytelling.
Add to that a compelling story which grapples with a variety of complex themes and interesting characters and you have a work of lasting cinematic value.
Meanwhile, you have in the US a long-standing perception of animated feature films as "kids' movies", due in no small part due to the dominance of Disney and Warner-Brothers in using the medium precisely for that purpose, to great effect. When Akira hit the US market it introduced a lot of people to animated movies that were mature, complex, had very high production and artistic value, and were very much not just for kids. It also introduced Americans to a manga/anime aesthetic which had been developing and maturing for decades but was relatively unknown outside of Japan.
It helped that Akira was an action film aimed at adults and teens rather than a TV show (which would require much greater investment) or a comedy/drama (which tends to have themes that are more culturally specific). This made the material a lot more accessible (even if you miss the story entirely the action is still entertaining, and the investment is only ~2 hours of time, the same reasons why US made blockbuster action movies tend to be very successful internationally as well).
Akira was a landmark within the anime genre, helping to propel anime and manga to even greater heights locally. It's no surprise that it ended up serving as the poster child for anime enthusiasm outside of Japan for quite some time. It was an impressive film and an impressive artistic achievement in its own right, in any genre, and that resulted in a huge amount of attention. That attention led some towards curiosity in the anime/manga genre which helped form the kernel of enthusiasm for the genres in the US and elsewhere.
As with most cultural phenomena it's difficult to make a definitive judgment, but the evidence is very suggestive.
You got a good answer from rocketsocks on what makes Akira a unique film. I'd like to explore the other part of your question, the Western view of anime pre-Akira, and more briefly how Akira was received in the West.
Anime profited enormously from two important developments in the 1980s: the VCR and its related technologies, and the growth of the Japanese economy. In its nascent stages (in the West), anime television series were imported generally into tv programming blocks like Saturday morning cartoons or latenight weekday cable. Despite some relatively sophisticated and ambitious storylines, series such as "Star Blazers" had extremely low production values; this, combined with Westerners regarding animation generally as a children's medium, ensured that anime received little exposure, except to certain niche groups (the true niche-ness of which may be hard to truly appreciate today), like college students and science fiction fans. Many early viewers of anime did not necessarily realize they were viewing a Japanese product, as early films and shows were heavily dubbed and edited to erase cultural markers. Anime viewers began bringing videos of shows like "Star Blazers" to science fiction conventions in the late 1970s, where they were not taken very seriously. It is not difficult to understand why: the editing of early anime was so nonsensical, and compared to Western productions, their visuals so poor, that most people who saw anime could not make sense of what a given series was about. Japanese cartoons were widely perceived, when at all, as simplistic, crude, and/or perverted, thanks to poor adapting and editing, and a certain hysteria surrounding the pornographic proclivities of certain monsters (Overfiend).
Susan Napier marks the film "Yamato" as a particular watershed moment in the acceptance of anime into science fiction conventions. With its clear cultural markers, "Yamato" is very obviously a Japanese product. During a science fiction convention in Baltimore,
"'Yamato' was to be shown after a screening of 'The Right Stuff'.... but 'The Right Stuff' proved so popular that fans clamored to see it again, setting up a confrontation with the 'Yamato' fans' waiting for their turn. [...] 'The Right Stuff' fans sneered at the very notion of the 'Yamato' series, asking why anyone would want to see 'some militaristic Japanese cartoon.' Ultimately, a compromise was reached, and the 'Yamato' film was shown well after midnight. And then it was shown again, and again."
The rise of VCR recordings helped promote anime at more conventions in the 1980s, where small groups would advertise viewings of "Japanese cartoons" in their hotel rooms.
"There was also... the particular pleasure of being part of a small and very specialized community of cognoscenti. The vision of a small group of fans gathering around a scratchy videotape [which was often not dubbed or subtitled, and "translated" by anyone in the room who knew a bit of Japanese or who had received a basic plot description] at a science-fiction convention also suggests a form of ritual, something that commentators on fandom have frequently mentioned as an important part of the appeal of fan subculture."
The VCR helped anime be distributed in this way, and also allowed Japanese producers the technological and financial freedom to create more episodes, and OVAs (Original Video Animation), which were designed exclusively for home viewing rather than television. This, combined with the growth of the Japanese economy, cultivated an atmosphere of experimentation and creativity that helped boost anime production values; the recession in the 1990s may have slowed this, but Napier writes that the dissatisfaction with corporate culture may have encouraged young artists to actually FURTHER pursue anime and manga production.
With the growth of the internet, anime dissemination became even easier for Westerners. As far back as 1994, anime fans were considered the most developed internet-based subculture (according to Wired magazine). The relationship between anime and the internet is a significant reason-- perhaps THE significant reason-- why anime has become as mainstream as it is today.
As for Akira's role in all this, I think it is important to stress Akira as a film, rather than a television series. This allowed it to have a widespread, mainstream distribution, rather than be relegated to television (let us remember how recently television has been taken seriously as an "art form"). Akira was also at the vanguard of the "cyberpunk" aesthetic, which I think is important to note. But significantly, Akira was also taken seriously by film critics: Roger Ebert made it his pick of the week when it was released. It was not a smash hit, but a "cult" success, aided once again by VCR bootlegs and convention culture, and its ensuing trickle-down effects, wherein members of science fiction or anime clubs based in universities or convention attendees became fans, and later filmmakers, authors, and designers. This influence, developed over a decade and eventually leading to Akira's wide rerelease in cinemas in 2001 (boosted no doubt by the success of The Matrix in particular), has certainly been helpful in making Akira so significant.
Source: Susan J. Napier, From Impressionism to Anime (2007)
What exactly do you mean by "development of anime in the West?" Is that western animation inspired by anime? The development and growth of imported anime? The development of the anime fan base? The use of Japanese animation studios for western cartoons?