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 You can stream torrents, most clients have an option to download from beginning and end instead of randomly so you can play the video directly after starting the download, just not possible to forward etc, but maybe it would be possible to do this too?👀 
 The random order adds to the speed, if you take that away, the file download will be slower, or at least will need more seeders. Why would you use torrent in that case anyway, a simple mirroring system would be enough. Mirrorlists allow for updating the list of "currently online hosts", linux package repos use this setup, and it's very reliable.

As for random seek (what you describe at the end), you need an index. AFAIK, an index can't really work without the complete file.

Technology enables a lot of things, but it's not magic, can't really make things happen that are physically impossible. 
 I understand that taking away the random order makes it slower but still like the idea of torrents because of the big amount of available clients / implementations already available. 
Was wondering how YouTube etc do the random seek as they don't have do download the whole file for that either, maybe it would be possible to do something similar with torrents, idk. You know the file size, and length of the video from headers, so you could tell the torrent client to download from byte X which should be around minute Y of the video.
I'm not very knowledgeable about torrents in detail, so thanks for the input.