This isn't actually a new argument, even in book form; Richard Corliss made the same argument in his book Talking Pictures, where he evaluated the work and style of several prolific Hollywood screenwriters.
This approach to evaluating movies has its positive and negative sides. It's true that the auteur theory puts way too much emphasis on the visual style of a film as opposed to what is in the script, as if the director is most successful when he's working against the script. (The early auteurists had a particular fondness for movies where a director brought a lot of visual flair to a terrible script, like Nicholas Ray did to a movie like Party Girl; it was considered the ultimate triumph of the director's art to make something out of nothing, rather than make a good movie from a good script.) The fact is that most movies pretty much resemble what's in the final script, and most good movies start with good scripts.
The problem with developing an auteur theory of screenwriting is that most screenplays are, in practice, not products of a writer's vision, even the relatively few produced screenplays that are entirely the original creation of one screenwriter. A movie usually has a supervisor, someone who is guiding the way the final product turns out; sometimes it's the director, sometimes it's the producer, and sometimes there's a tug-of-war between the producer and the director. But whoever is in charge is usually going to have an idea of what he wants the movie to be like -- and that means that he is going to want a script that fits his idea of what the movie should be. He's either going to have the screenwriter rewrite the script until it fits his conception, or he'll bring in other writers to get it the way he wants it. The end result is that the writer is not writing to serve his or her own vision, but someone else's; screenwriting is usually done to someone else's specifications.
An obvious example is Casablanca. The man in charge of the movie was the producer, Hal Wallis. He bought an unproduced play, assigned three screenwriters to work on adapting it for the screen (Julius and Philip Epstein and Howard Koch), had them rewrite each other's material, did some rewriting of his own, brought in other, uncredited writers to tweak it. The final script is a mish-mash of many different contributions, but all the contributions were made in the service of what Hal Wallis wanted the movie to be. It makes sense to say that the finished product reflects his vision even if he didn't do most of the actual writing.
Or take Frank Nugent, the former New York Times movie critic who wrote most of John Ford's best post-WWII films (including Fort Apache, She Wore a Yellow Ribbon, The Quiet Man and The Searchers). In a letter to filmmaker/critic Lindsay Anderson, he explained his working relationship with his director (and father-in-law) Ford:
Ford works very, very closely with the writer or writers. . . . Usually a script is written scene by scene, gone over, discussed, rewritten maybe, then okayed. . . . The finished picture is always Ford's, never the writer's.
Obviously the identity of the writer makes a difference -- Nugent did terrific work for Ford, and other screenwriters often didn't do as well. But it's clear that the scripts were written to Ford's specifications, not Nugent's; the writer was not being paid to express his own creative vision, but to help express someone else's.
Are there auteur screenwriters? Sure. Some non-directing, non-producing writers have such a degree of control over their scripts, and such a strong style and creative personality, that the film reflects their vision as much as the director's or producer's. Auteur screenwriters would include Jacques Prévert (Children of Paradise), Paddy Chayefsky, and, before he became a director, Preston Sturges. But for the most part, a screenwriter is a means to an end; he or she is working to carry out someone else's goals, be it the director's the producer's, or the studio's. That's not meant to put down writers, nor to justify the way they're traditionally treated in the film industry (barred from the set, treated as interchangeable), but it's part of the nature of moviemaking.