1. they made streaming a free add on to DVDs to get people using the service, which resulted in streaming becoming popular.
2. The media owners started to (or perhaps always had) cut their deals with Netflix on a per subscriber basis rather than per view. So Netflix was paying the networks for everyone who subscribed, including evyone who only watched DVDs. This became unsustainable.
3. So, they needed to separate these people, thus the split.
I honestly don't see how they could have handled this differently, they needed to tack the service on to DVDs to get people on board, and they needed the services to be separate to actually make money on streaming long term. It might have worked if they had been able to pay for videos on a per view basis, but I'm not sure they have the clout to make that happen.