Hollywood is rapidly taking sides on it. Peter Jackson, Steven Spielberg, Ron Howard, JJ Abrams and Martin Scorsese are already shareholders, while Christopher Nolan and James Cameron are firmly in the "anti" camp.
You can expect the arguments to rumble on for some time.
The scheme's fans, like Jackson, argue that it will "expand the audience for a movie". Parents of young children, for instance, who would never customarily manage the trip out, would find themselves in a position to watch new releases. Jackson sees a "critical point of difference" with earlier attempts to collapse the window between theatrical and home-viewing debuts.
"It does not play studios off against [cinema] owners," he says of Screening Room.
"It respects both and is structured to support the long-term health of exhibitors and distributors, resulting in greater sustainability for the wider film industry."
The anti brigade are wary of a paradigm shift, though.
Cinema owners obviously fear a reduction in the all-important selling of popcorn and soft drinks - the mark-up on these, often an exorbitant 85 per cent, makes a critical difference to their profit margins, since studios can receive as much as 90-95 per cent of the gross ticket sales in the first week.
Cinemas are already fighting to hold on to their footfall, with the proliferation of home-viewing platforms, blockbuster TV series and the narrowing of the window between cinema release and rental.
Isn't this yet another reason to stay at home? Cinema theatre owners such as the Art House Convergence (AHC), a US organisation comprising 600 different businesses, certainly think so.
They issued a stern open letter about the potential economic impact of Parker's proposal. The UK's Cinema Association has also weighed in, calling it "a massive risk".
Parker and his co-backer, the music executive Prem Akkaraju, have none the less been canny about recruiting support, partly by proposing to allocate as much as $20 out of each $50 rental to the cinema chains, and sweetening the deal for cash-strapped consumers with free cinema tickets thrown in.
This would offset what may sound like a steep rental cost, but some analysts view the price as too low, pointing out that it would be possible for 10 teenage girls to hold a sleepover screening of Frozen 2 at a cost of just $5 each: good value for families, but "cannibalisation" for the industry.
Previously, the only device studios would permit to download (rather than stream) first-run films was a monster of a thing called PRIMA Cinema, which cost a pretty $35,000 plus film rental fees of $500, making it singularly unlikely to threaten the mass-market dollars the cinema industry depends on.
The Screening Room idea has prompted renewed debate about whether the primacy of the film-going experience is heading further into a slump. Hugh Jackman and Taron Egerton, the two stars of Eddie the Eagle, recently got into a debate about this while recording an on-camera promotional interview.
Jackman voiced his opinion that filmmakers need to find fresh reasons to get audiences into the cinema; Egerton was concerned that "shared experience" would fall by the wayside if Screening Room panned out.
There's much talk about the "special" value of a cinema outing, but Jackman has a point - there's nothing all that special about being among patrons checking their phones, rustling around in crisp bags, or talking in a puny multiplex screen.
There's having a communal experience that truly enhances the film, and then there's the kind that makes you want to quail and run back to bed.
Cinema owners are perhaps missing one upside of Parker's idea, which is the potential it might have to rescue a certain category of underperforming theatrical releases from commercial failure. There's the example of Sacha Baron Cohen's Grimsby, released in the USA as The Brothers Grimsby, which has only managed to drum up a measly $6 million there over a two-week frame, despite getting a Borat-level thumbs-up from the exit poll Cinemascore.
It simply didn't have "event" buzz, but Screening Room rentals wouldn't depend on that. It could be a godsend for the Grimsbys of this world - or for modest prestige fare such as Room, Spotlight, or 45 Years, which did very nicely indeed on its British video-on-demand release.
Still, regardless of the audiovisual wow factor that will doubtless tempt Avatar fans to see its sequels on the biggest screen they can find, there's a lot to be said for the collective, among-strangers experience, even when you're watching a low-budget drama about a mother and son being abused in a garden shed. Beyond the economics, the whole ethos of filmgoing will cease to exist if home viewing becomes the gold standard.
A quick poll among friends revealed relatively few who would leap on the Screening Room idea - or only in certain circumstances, such as having young children, owning a high-spec media room, or perhaps living far from urban centres or multiplexes.
"Potentially bloody great for parents," was the most enthusiastic response; "I would never, ever pay for this," said the most bullishly unimpressed. Few thought the price was especially steep when divided a few ways, though "passing a begging bowl around" wasn't everyone's idea of fun.
From the sounds of it, we've got some way to go before the future of the big-screen night out looks truly endangered.
A place like the Prince Charles Cinema, in London's Leicester Square, is a great model for getting back to what cinema is all about.
Their 35mm and 70mm screenings, typically of cult classics that are often available to stream at home anyway, are wildly popular and regularly sell out.
Venturing along for John Carpenter's Big Trouble in Little China (1986) recently, it was hard to imagine a more convivial screening.
It combined the best of both worlds: a cosy night-in-with-your-mates vibe, crossed with the excitement and atmosphere of a packed-out, like-minded communal nostalgia trip.
It's a film I grew up on, replayed countless times on VHS in my early teens. And there, at the same screening, was my younger brother, who just happened to have lured along a group of his own.
When cinema can foster a feeling of togetherness through that kind of rare serendipity, there's no way home viewing will ever entirely replace it.
