I don't think the Apple case can be compared to Kodak's film business. Apple may have failed to innovate, but this was in the context of computing - a massive next generation wave. Analog photography is exactly the opposite. The vast majority of potential photographers will not be convinced to choose film over digital, no matter how many TMY-2 commercials Kodak decides to run during the superbowl, or how much R&D they dump into making TMax 100 even finer grained.
As for improvement, well, obviously anything can be improved if the investments are made, but that has to be justified by potential demand or you're sunk. If film was still the big thing, Kodak would obviously still be doing what they did all those years at KRL, funding massive R&D and putting out products we probably wouldn't even recognize. By now you might have an ISO 1600 film with finer grain than TMax 100, radically different chemicals, a wide selection of papers, etc. But you can't constantly pour money into innovation when the market for the product is tiny, and already well served. In that sense, again the car analogy is a red herring. Car companies innovate because everyone buys cars. Very few people buy film. Even fewer print negatives in a darkroom. In that context, no, improvements are not required.
Further, such improvements take time. The digital world moves too fast. Suppose Kodak introduced the sharpest, finest grained film ever, with an ISO of 3200. Yeah that's pretty cool for us on APUG. But high end digital cameras have already gone way past that kind of speed. Not to mention more and more people will likely continue to abandon the idea of the purpose-built camera altogether. They'll use their phones, or some wearable technology.