Product feature suggestions don’t really belong in this forum, they should be directed at feedback@twitch.tv.
However, we appreciate your thoughtful suggestion, so I’ll go ahead and address it 
We currently stream over RTMP and so our player has no knowledge of past video. We are in the process of moving over to HLS to serve video, which serves streams in little 4 second chunks. Once we’ve finished this migration, it should be a piece of cake for us to add in this delayed stream mode functionality.