It would never work today, because the model for movie-going has changed so drastically.
Prior to 1960, going to the movies was really much more like watching television. You would pay your admission, and then you could sit in the audience and watch for as long as you liked. You might come in during the middle of a feature, watch the newsreels and a couple of cartoons once it was over, watch the beginning of another feature and then go home. It was a very casual experience, which is part of what led to its enormous popularity. You could go in and out, you could talk during the movie, you could get food. This is part of the reason why, at least in America, it took so long for film to be seen as an art form. It was considered extremely low-brow.
By 1960, though, you started to see the rise of the auteur director. This isn't to knock the efforts of directors under the studio system, a great deal of art was produced during that time in spite of the way the system was set up. At this point, though, American filmmakers started becoming more conscious of film as art, though.
The man who might be most directly responsible for the complete death of the movie serial is Alfred Hitchcock, since he deliberately changed the way American audiences watched films with the release of Psycho. It was just the typical hyperbole of "this movie is so good it will change the way you watch movies!" Psycho was released with explicit instructions not to allow anyone into the theater once the film had started. This was a radical shift in how movies were presented, but it was vital to preserving the film's massive plot twist.
Obviously, later films followed suit to capitalize on Psycho's success, to the point where this is the only way we think about going to the theater anymore. Television and a internet downloading have become the substitutes for the old movie system, and those are the only places where the serial model can really succeed in the modern world. Even in television, that model is starting to fall apart, because people would rather watch an in-depth serial on their own terms, on DVD or iTunes.