Would be cool but not going to happen.
It'd take up too much space. And saving that many films would not only bog down internet speed but also cause internet caps be reached even faster.
Keep in mind that most (non quiting) players each play on average of 5+ games a hour. Multiply thelat by the number of players for each game and...well you see where I'm going with this.

There's also the Upload Studio thing to take into account as well as Twitch. I believe Theatre mode will return but we'll not be able to upload full games. Just 5 minutes max, at a time. And that alrwady takes half an hour or so to upload. Which is weird by itself.
If you want to upload a full game, then Twitch saving would be your best bet.
Now if only I can figure out how to edit and save those Twitch videos for later viewing.