When Warner Bros. Digital Networks announced a week ago that the company was shuttering FilmStruck, a streaming site devoted to classic, foreign and hard-to-find films, its small but mighty band of subscribers first plunged into despair, then flew into action. At this writing, more than 12,000 people have signed a Change.org petition to save FilmStruck, which was an initiative of Turner Classic Movies.

What’s at stake isn’t the arcane purview of a handful of film buffs, but a nation’s legacy, an industry’s institutional memory and an art form’s creative future.

The news of FilmStruck’s scheduled demise at the end of November might have come as a shock, but it wasn’t necessarily a surprise. It was clearly anticipated this past summer with the purchase of Time Warner by AT&T, which has made no secret of its skepticism when it comes to the value of boutique markets.

“I want more hours of engagement,” John Stankey, a longtime AT&T executive now in charge of Warner Media, told HBO chief Richard Plepler at a town hall meeting last June. “Why are more hours of engagement important? Because you get more data and information about a customer that then allows you to do things like monetize through alternate models of advertising as well as subscriptions, which I think is very important to play in tomorrow’s world.”

Translation: Niche was nice. But volume is the future.

The disheartening fate of FilmStruck illuminates not just the churn and change cinema is enduring but also some of the medium’s eternal truths. It’s easy to forget that the obscure films by Yasujiro Ozu, Jean Vigo and Orson Welles that FilmStruck offered have, for most of their afterlives, been available only rarely, through the heroic preservation and advocacy efforts of libraries, museums, academies and film archives. It’s a function of how quickly we internalized the Web’s we-want-everything-and-we-want-it-now ethic that we forgot that FilmStruck’s two-year run was a relative blip.

Thankfully, those institutions are still committed to exhibiting classic and rarely seen movies. The importance of that mission was palpable last week at the launch of the Smithsonian African American Film Festival at the National Museum of African American History and Culture. The opening night and closing night films were the upcoming releases “Widows” and “If Beale Street Could Talk.” But the ballast of the festival’s programming was dedicated to films from the museum’s collection, as well as programs from around the country, films that constituted not just a priceless social history but a vitally important artistic canon.

Gathering at the museum and the Freer Gallery to watch Lebert Bethune’s 1964 documentary “Malcolm X: Struggle for Freedom,” Madeline Anderson’s “Integration Report One” (1960) and “The Fight,” William Greaves’s stunning 1974 chronicle of Muhammad Ali and Joe Frazier’s historic 1971 boxing match, reinforced that nothing beats seeing a film in its original format, with a group, in the spirit of aesthetic discovery and shared patrimony.

Of course, those of us who value seeing film in that context are spoiled for choice in Washington, where significant contemporary and historic movies can be seen in nearly every museum, cultural institution and embassy, not to mention local festivals and independent cinemas such as the Avalon and AFI Silver Theatre. (For a perfectly delightful example, look no further than Friday night’s AFI screening of short films featuring the silent-film comedian Alice Howell.) The great public service of sites such as FilmStruck — as well as Kanopy, which is available through public libraries, and Fandor, which is dedicated to indie films — is allowing exponentially more people to savor what had previously been available only to a lucky few.

Interestingly enough, one of Washington’s most important film institutions, the Library of Congress, has announced a new initiative: the National Screening Room, a streaming site currently showing 299 gems from the library’s vast moving image collection (and they’ll be adding more every month). Among the late 19th- and early 20th-century works on view are films by Edwin S. Porter, D.W. Griffith and, just in time for the Halloween season, the 1910 adaptation of “Frankenstein,” produced by Thomas Edison.

The silvery nitrate images of the National Screening Room play across the computer screen like messages beamed from a time both ancient and miraculously immediate. Watching Mary Pickford and Marion Leonard get blitzed out of their minds and suffer the bleary-eyed consequences in the silent 1909 comedy “The Day After” is to realize how little our ideas of visual entertainment have changed over the course of a century. D.W. Griffith, meet “The Hangover.”

It’s just that connection to the past, with its sense of continuum and mutual influence, that is missing from Warner Media’s shortsighted decision to jettison FilmStruck. Granted, some of the site’s offerings may find a secure home: the thoughtfully curated Criterion Collection, once available on Hulu, will likely land elsewhere. But Warner doesn’t seem to perceive the value of its own holdings, outside branded intellectual property that can be easily monetized. Whether the studio will lovingly and prominently present its own archive when it launches its exclusive streaming site remains to be seen, but its dismissive attitude toward FilmStruck doesn’t bode well.

Could streaming behemoths do better? Just this week, Amazon released a remake of Dario Argento’s 1977 cult horror film “Suspiria.” (Amazon founder Jeffrey P. Bezos owns The Washington Post.) Netflix is bringing out “The Other Side of the Wind,” Orson Welles’s final, famously unfinished film. Both arrive burnished by cinematic legend and the patina of connoisseurship. But neither would be meaningful without an audience enriched by a working knowledge of their provenance and artistic legacies. If Netflix or Amazon were to acquire FilmStruck — the equivalent of making space within their vast virtual libraries for a rare book room — they would be investing in the visual literacy of their own customer base and, by extension, their own cultural capital as image-makers.

And it’s not just spectators who need that education: The artists that studios and especially streaming platforms are courting with profligate amounts of money won’t be able to create a vibrant, new film language without a firm footing in fundamentals that go back way further than “Pulp Fiction” or “Star Wars.”

As it pinballs from one dizzying technological shift to another, Hollywood can’t possibly build a viable future without robustly embracing and promoting its past — and not just by paying it sentimental lip service. The difference will be all the more apparent as the industry embarks on yet another awards season, when it can be counted on to cover itself in glory and self-referential nostalgia while celebrating its finest achievements.

You can bet that Warner Bros. will be a part of the scrum: Its big Oscar movie this year is “A Star Is Born,” the fourth remake of a movie steeped in American cinema’s most enduring myths about art, celebrity and self-sacrifice. While the studio sends director Bradley Cooper and co-star Lady Gaga out to campaign this season, fans might want to bear in mind that the very first iteration of the story was a 1932 movie called “What Price Hollywood?” by George Cukor. It’s available on FilmStruck. But not for much longer.