Yeah, film stock and the various toxic chemicals used for developing film is more natural than the little electrons running around inside your colour grading workstation, I get it.
And the big question: are you watching the film on digital equipment, or on an old analog TV or movie projector?
Natural is perhaps not the word to use but there is a clear visual difference between analog and digital film and color timing and color grading, just as there's a difference between music that was recorded and mixed with analog equipment, music that was recorded with analog equipment and mixed digitally, and music that was recorded and mixed with digital equipment (all observable while listening to it on a digital medium, though sure it will sound different on an analog medium too).
Yeah, I'm well aware of these various analog artifacts, both in photography and audio work (which both happen to be on my long list of hobbies, indicentally), so I'm in agreement with you.
It just amuses me to no end when someone claims analog processing is "natural", while digital is... "unnatural" then, I guess? Maybe the pleasing saturation and non-linear characteristics inherent to analog mediums (film, magnetic tape, etc.) can be considered natural, but they are really just euphonic distortions of the original signal that we tend to like (and it's probably more of a learned response through familiarity than the "analog representation" being "inherently better").
These analog processes can be (and are) analysed, understood, and replicated in the digital realm; they are just effects, after all. You can replicate film stock with 90%+ accuracy with pure digital processes on purely digital footage, I'd say. (Whether people do that, or just apply some simplistic digital processing that looks like shit is a different matter...)
But yeah, it can be easier to just apply the "stock effect preset" by using a certain analog medium or process... as long as those analog mediums and equipment are still available and functional. This is one of the reasons why I put a lot of importance on emulating old sound cards, CRT displays, etc. accurately. The day is close when eventually all will die, and there won't be any replacements (well, at least not for CRTs, that's almost guaranteed).
(And if it's still not clear, I'm a big fan of "analog". But for the most part, the future is digital; most of these analog processes can only survive in the form of emulated processes as digital algorithms going forward, whether we like it or not.)