Torrent streaming has a lot of scaling issues that you've just been lucky enough to avoid. A new torrent will have issues with its initial seeding. A new torrent is limited to the seed bandwidth of whatever seeds have the complete file. The initial members of a swarm can't help each other because they're all downloading the file sequentially so can't really share with one another. They only increase seed bandwidth to subsequent participants in a swarm and only so long as they seed the content.
In the traditional BT model swarm participants download blocks out of order so they can share them with peers. So even the initial members of a swarm can share with one another. Streaming requiring blocks be received in sequential order breaks that peer amplification.
With torrent streaming unpopular content and new content can easily stall or just never begin playback. At a small scale torrent streaming is workable but it quickly starts requiring a lot of infrastructure costs. Long tail content on BitTorrent is virtually impossible to find as popularity required for availability.
Sure, you could do something like you mentioned, but doing this for every single video is not likely to go well. But very clever! And helpful, I'm sure. Not a true solution most of the time.
I do very much enjoy the Chrome side-scrolling dinosaur game that appears when I'm offline, but I don't enjoy it more than once every few weeks :)