Analogue systems are not intrinsically better than digital ones, but they are tied up in the complex history of what sounds and images mean to us and explain why they, and the 'film look', remain so important.
Why do we still want moving images 'to look like film'? Just what is the appeal of the 'film look'? The answer is complex; some of it is nostalgia and some of it is myth. Some of the appeal is due to film's actual technical advantages, but a lot is down to elements that have nothing to do with fidelity or technical superiority.
How we got here
Video was always seen as poor cousin to film because for a long time video cameras, particularly portable video cameras, just weren't very good. Video couldn't compete with the dynamic range of film. Highlights would burn out, shadow detail would be lost and the apparent crispness of the image was dependent on sharpening circuits that effectively drew lines around objects to separate them. Turn down the sharpening on a broadcast standard BetaCam and you'd see just how soft the image really was. Film, in comparison, showed more detail in a subtler, more natural way.
Over the years, video got better and better, but it was only with large sensor digital cameras that it could really compete with and exceed the qualities of film. Large sensors also gave video cameras the shallow depth of field previously associated with cinema. It wasn't until the 21st century that it dawned on the video world that shallow depth of field was one of the key elements of the movie 'look'. Depth of Field adapters, which focused an image onto a ground glass screen (a sort of ersatz large sensor) in front of the camera lens, had a brief moment of glory until they became more or less obsolete with the rise of the DSLR.
That damaged look
Much of the appeal of film is due its associations - formative experiences watching great movies in cinemas or actually working with the stuff itself. We can't undo these emotional connotations, and they are as real as any more quantifiable elements. But let's not forget that many of the characteristics of film are actually its imperfections.
The 'film effect' filter built into QuickTime and other programmes on your home computer creates a sort of parody of film; it is grain, jitter and scratches that are emulated. A clear case of the appeal of film's imperfections was the use of Super 8mm, which went through a phase of great popularity in rock videos because of its granular qualities. The late-lamented Kodachrome had a wonderful, bigger-than-life saturation, a fantasy evocation of world of blue blue skies and golden beaches. Here was a 'look' - evocative and not totally predictable, intrinsic to a particular technology. And why did we like it? Partly nostalgia, of course, but also, perhaps, because we like imperfect images because they allow the imagination to intervene.
Here's a parallel legacy of the analogue age in the audio world: the guitar amp. All serious guitar amplifiers now are valve driven; only the cheap mass produced amplifiers are solid state (often equipped with digital emulation that allows you to switch from a 'Fender' to a 'Marshall'). This is not because valves are better at reproducing sound; it is because their distortion, particularly when overdriven, adds complex harmonics to the relatively characterless output of an electric guitar. The Vox AC30, perhaps the most famous guitar amp still in production, first appeared in 1958. There is nothing clever about its design (a basic valve amp with a speaker that originated in the 1930s), but it helped to create the guitar sound of the 60s. The Marshall amp was a cheap British emulation of the Fender using UK valves, but when Jimi Hendrix turned every knob on it up to maximum, something miraculous occurred. Nowadays, bands use a small, characterful, valve guitar amp miked into a massive solid state PA system - a little like shooting on Super 8 and scanning it to 4K.
Of course, you can fake the look of Super 8 with digital techniques just as you can fake a valve sound, but those who can afford it want to go for the real thing, even if what you get is a much more limited range of effects. This is applicable to the high-end of film production too: if you are experienced in working with film, you know what you are going to get; 'the look' is built-in to the tools your are using.
The creative struggle
And here, I think, is a key point about the revival of interest in 'outmoded' analogue systems - artists need both limitations and random elements. Some of the most creative moments happen when you are struggling against what the equipment you are using will actually do, when you are pushing it to the limits. It is not all about control, you may value a medium that brings with it its own particular qualities, rather than having an ability to emulate anything. (I will resist an anecdote here about having a relationship with an actress). When you turn up the gain on an amp or overexpose or underexpose a film stock, something quite wonderful and not wholly predictable might happen.