"Consumers weren't looking for Reed to get out of the DVD business. They were just looking for more streaming content." — Michael Pachter, Wedbush Research
This, I think, hits the nail on the head. In the wake of Steve Jobs' passing there's been a lot of discussion about his management philosophy. One of the pillars of that philosophy is that you need to re-invent what you do before someone else does. This empowers Apple to to kill off a current product before its been fully milked and replace it with the next great thing.
Reed Hastings was trying to do the same thing, but he failed to grasp the key difference above. When Apple releases a new generation of product it always improves on what was available previously: It costs about the same, or less, but it provides an improved experience through more capabilities and/or a better form factor. Splitting Netflix both cost more and degraded the experience for everyone. People just wanted a better streaming service, not a company split in half.