Note that subtitles and closed captioning aren't the same thing. Subtitles are text in a language other than the one on the audio track of the film. Netflix does subtitles in English for foreign language films. Closed captioning is a service for the hearing impaired that can be turned on by the viewer if needed. Netflix, or any other streaming service I know of, can't do that.
That's right, the technology for streaming can't do closed captioning, and you would have to have hardware to support it to. The Roku would have to pass the CC to the TV for display. CC is always on the signal you get from the OTA, Cable, Satellite and you select to display it or not on the TV as far as I know. It is probably pretty far away from being able to do CC for streaming video. Do DVDs have Closed Captioning? Anyone know?