I should mention some previous/existing projects which in some sense bear a strong similarity to this idea. Corrections and additions wanted.
Sita Sings the Blues Distribution Project promotes (mainly active 2009-10?) distribution of one premium video, but aimed for replication. I suspect replication requires more centralization, ie a platform like proposed here.
ClearBits, formerly LegalTorrents, operated 2003-2013, provided bittorrent hosting for and promotion of CC licensed material (some libre) including movies. It did not provide a viewing experience, but was a go-to place for premium publicly licensed material. Web pages for several existing premium libre videos still refer to the service, though it has been down for 2 years.
VODO started off distributing CC licensed (but none libre as far as I know) premium video via Bittorrent, but appears to have branched out to include indie films under other terms (aside: what does "P2P-exclusive" mean?) and selling bundles of indie game/video/audio/etc material. Their blog is down, but http://web.archive.org/web/20130124194812/http://blog.vodo.net/?p=300 highlighted some of their success and noted dedicating 5% of their revenues to a "Free Film Fund"; unclear what came of that. http://vodo.net/about/ emphasizes bundles and says they are working on a new product called "Black Box". I suspect VODO's aggregated audience for indie material is too diffuse and has too many other places to go, but nevertheless VODO may be a success on its own terms. This idea instead aims to aggregate a much more focused and demanding audience; its 'limitation' to only libre video may make for a more potent community and intervention.
Participatory Culture Foundation had various projects (mostly under Miro name) for aggregating feeds of video available gratis on the web -- vastly more diffuse selection and audience than VODO, but still an interesting attempt to create a popular alternative to proprietary distribution channels for premium video.
The Internet Archive hosts any video that belongs in a library and that it can get away with, including premium libre video. This is an incredibly valuable service, but by itself does not aggregate an audience and beneficient cycle of demand for premium libre video (but as Jon Phillips noted above, could be a good backend or partner in some way). Though they are very different (non/for-profit, scale, excise "that belongs in a library"), the rest is true of YouTube as well.
The Public Domain Review film collection, much of it hosted at the Internet Archive, is an example of a focused viewing experience, but obviously does not directly help grow a contemporary libre film audience.
Wikimedia Commons hosts only libre videos, some small number of them "premium" and has some mechanisms for promoting the highest quality material. This is probably by far the most promising of existing projects due to its libre focus and community curation. Its focus is on material useful in an encyclopedic context rather than entertainment a la Netflix. I suspect a libre platform focused on the latter would be a useful intervention, thus this idea.
Blender Cloud hosts the Blender open movies with enhanced access for $10/month, funding further work. It is more of a behind-the-scenes platform than a viewing platform. The Blender universe including software, community, foundation, cloud, movies...is the most vibrant and coherent part of the otherwise diffuse libre premium video world. Anything Blender does is strongly complementary.
FreeGameDev network, because games bear some similarity to video, see analysis.