I worked at a streaming company once, building up its technology, but that company was such a bad experience that I don't feel like joining a streaming service for anything. It would just remind me of that bad time.
The video game market also has a schism between physical media and digital downloads...
Even with games on physical discs that you would "buy", it is common that there is a DRM scheme where it tries to contact a server over the Internet every now and then, or it won't start. No Internet connection, or reinstall on a different computer: no game. Once the game publisher discontinues the DRM server, you can no longer play the game you "bought". This means that there is no second-hand market so there is no way to collect them, you can no longer play old games on your new computer ... and some games can not be (legally) played by anyone anymore because the game publisher has discontinued the DRM server. Such a waste ...
There have been a few attempts at similar schemes for movies on physical discs but thankfully they haven't taken off.
I'm afraid that if you have a streaming-device and a movie downloaded to its hard disc that you would risk getting into the same problem that some games have: that some time, it would just stop playing because the rights-holder has discontinued (or maybe just reconfigured) its DRM server.