Yea best performance would be the player is always a few seconds behind so that optimal buffering levels are maintained. Different lag times for each chunk might make the playback seem a little choppy. So that is another reason for a player that understands its a live stream. Quite likely a one second delay behind the actual live stream would be a good point allowing some buffering without being too far behind allowing interaction with the streamer like a youtube live stream with their side chat running
Well if it is one byte out then its a different chunk. But if you just inserted in the data map whole chunks from the original then yes it would become a very efficient use of storage. How many milli seconds (or seconds) would a chunk represent for say 1080p30 stream? That would be the quantisation if keeping chunk boundaries for a segment of video.
But this may not work since syncing could be an issue. Key frames and all that.
Maybe a special writer could be developed that started each key frame on a new chunk. No increase in storage size, just some chunks (ones just before key frame) are small when new key frame occurs. This would have an increase in store cost due to extra chunks being written