Just to share my personal experience: My wife and I have been Netflix customers for years. Streaming is pretty convenient for us, but two major problems: 1) lack of content and 2) lack of subtitles / closed captions. Captions are important because we watch movies at night, after the kids are in bed. That means we keep things are quiet enough that you occasionally miss a line of dialog. Because of those two issues we're back to DVDs in the mail. Here's my point:

While the services were integrated we could play with the online service (wait for it to improve) while still getting DVDs through the mail. It didn't cost any extra to try a streaming movie or two. Now that they are separate, checking up on the online service has a much higher cost, both monetarily and in terms of effort. Personally I'm disappointed, I liked streaming a lot, but for us it just wasn't quite there yet.

As others have said, the two services are complementary. I might like to know that I could watch a movie instantly instead of waiting for it in the mail, even if that's what I'd planned to do. Or that I could get a DVD in the mail because it isn't available for streaming.

As a customer I feel Netflix cares more about promoting streaming than keeping me as a customer. Rather than holding the door open so I can take my time converting to online content, I'm being pushed. Maybe right into a the arms of a competitor, because I'm not feeling the love from Netflix.