so the auteur theory was pioneered by French film buffs in the Cahiers du Cinema around the 1950s (though if often associated with the French "New Wave" of thd 1960s) and it reinvented many aspects of film criticism. This lead to a revolution which pushed directors much further out in front. I think Britannica has a good one sentence definition of the theory here:

The auteur theory, which was derived largely from Astruc's elucidation of the concept of caméra-stylo (“camera-pen”), holds that the director, who oversees all audio and visual elements of the motion picture, is more to be considered the “author” of the movie than is the writer of the screenplay

http://www.britannica.com/EBchecked/topic/44609/auteur-theory

one key difference is film is a visual medium, the Mise en scene is an important part of the work more so arguably than even the script.

essentially it was argued a director puts his firm stamp on all the films he makes and a good clear example of this is John Ford (who i'm told hated the theory and saw film as a collaborative effort-i can't source that though) which also highlights how this idea brings even non "high art" directors into its definition. I can't really talk about what existed before this but here's i think the key part of your answer

You are interested in the field of auteur theory.

https://en.wikipedia.org/wiki/Auteur_theory

As that article says, it's a concept that was popularised in the influential French film journal Cahiers du Cinéma in the 50s, though it had been something that had been talked about by some since the 40s. It was popularised in a time where a number of directors had successfully established themselves as imparting their own personal "brand" to films, there were directors like Hitchcock, Akira Kurosawa, etc who auteur theory claimed were "auteurs" and thus their films were studied as products of that director unlike films by other directors which didn't impart anything personal to the material from the screenwriter.

It's a concept that gradually trickled through to the UK and to America, being distilled and simplified down to just a general concept of thinking of the director as the primary author, and this remains extremely influential in the way people write about contemporary films and their directors, even though auteur theory itself suffered a lot of criticism for a long time now. We don't distinguish between auteur films and other films now, there's just kind of an implicit assumption that a film by any "known" directory is a product of that director.

The wikipedia article will point you to important writings from the period, such as

In his 1954 essay "Une certaine tendance du cinéma français" ("A certain tendency in French cinema"), François Truffaut coined the phrase "la politique des Auteurs", asserting that the worst of Jean Renoir's movies would always be more interesting than the best of the movies of Jean Delannoy. "Politique" might very well be translated as "policy" or "program"; it involves a conscious decision to value and look at films in a certain way. One might see it as the policy of treating any director that uses a personal style or a unique worldview as an Auteur.

I'm speaking more practically as a filmmaker whose worked in both network television and feature films.

Television and theater are both a writer's medium as they written and almost never deviate from the words on the page. Television started out primarily written like plays where any and all internal dialogue was translated out loud much like a play.

Non episodic film is more of a collaborative form of filmmaking necessitating technical and creative direction in the form of a director. While episodic television in the last fifteen years or so has begun adopting a single camera approach (meaning rather than a sitcom which utilizes four cameras on a soundstage), they still defer creative direction to the show runner and writers. This is for any number of reasons, but most practically, since a television show tells its story much slower and has different arcs and directions to go with characters that last for seasons, they have to steer the ship and can't let a director's personal choice interfere especially since director's don't typically shoot all of the episodes of a television show. This is to preserve the tone of the show under a singular vision.

A feature film has a script and that's the end of the writer's influence because all of the character arcs and plot is on the page. This gives the director the freedom to interpret the script however they choose rather than executing a writer's vision. Historically, the late 60s/70s were an important time in American cinema where auteurs were more widely celebrated.

To address your conducting question--since a composer writes a song to be performed the same way every time, the conductor is there to execute the composer's vision without any improvisation. Much like television.

Not really an answer but to put some different context to your question I'd argue that music isn't necessarily attributed to the writer. As far as orchestral music certainly, but more modern popular styles tend to be attributed to the performer (Elvis, for example, as far as I know didn't write any of his songs). Electronic music interestingly is usually attributed to the producer. So it would seem there's something specific about how different styles of media are made that tends to result in who gets the credit.

I believe that ignoring the director in theatre is a North American phenomenon. In France, the director ("metteur en scène") is a very important figure. This may have to do with the fact that so many plays staged today were written hundreds of years ago and have been performed literally millions of times (anything by Molière, Corneille, or Racine), so that it makes little sense to discuss the text, but a great deal of sense to discuss its interpretation.