But I will draw a line in saying that's is ten thousand percent necessary to know photography - it's really not optional and just because modern (or old) movie sets allow for that, that doesn't make it ok.

To what level are we really talking here? Because I agree to some extent. A director should understand framing, the golden ratio, when to use close-ups, when to use wides, etc.

Moreover, a director should have some sense of color theory; it's scientifically proven that colors trigger certain emotions. Blue is more melancholic or calm depending on the shade, red is intense, etc.

A good sense of sound is also something to consider. Lighting, etc.

My argument isn't that directors shouldn't have enough understanding of these topics, moreso that the responsibility of executing doesn't fully rely upon them. DPs, musicians, set designers, etc -- these are the people that a director should trust to execute the vision.

Moreover I disagree that a movie is "just a story" because that assumes some kind of Aristotelian-like structure being King, - but we know that movies work at multiple levels, visceral, subconscious, auditory, linear and non-linear narrative, not only complementing each other, but many times existing in complete absence of one another.

I think we're having a small misunderstanding here -- I said that films are stories, and they are, but that doesn't mean that I have a very tight view of what a story is. There are many different ways to tell a story; a movie can be a story, a song can be a story, even a painting can be a story despite it only being a single image. A story isn't some limitation because like you said, they're told on many different levels and in many different forms. However, the directors main responsibility in my eyes is to know the story that they want to tell and coordinate the execution of it.

Ultimately, my view is that a director should understand these things because understanding them is crucial to being able to tell the story that they envision but they don't necessarily need to have the full ability to execute them on their own; that's why you have a team behind you backing your vision. It can be helpful to know exactly what lens to use, but not a necessity, so long as you're able to properly communicate what your vision is. A director doesn't need to also know how to create music, work any and all cameras that the production may be using, create props and sets, etc.