That seems like a pretty good idea generally. For a single-player game an extra straight-to-stream output could even show extra info; be third person, etc.

Hell, why not include the ability to render locally, like a halo/StarCraft (and many other series of course, these are just the two I remember) replay.

The player still has to see the game and "watching your own stream" introduces significant (inconsistent) latency making it inappropriate for any game with timing.