I think the difference between PC gamers being okay with the "death of the box" and the same logic being applied to the consoles is, like you said, the lack of porting and permanence that comes with owning digitally downloadable games on the systems. You can still go buy Abe's Odysee on Steam and have it run on a modern machine, but imagine if it was only available as a digital download on an online system that's already gone under, like the original Xbox Live? Would that just be gone forever? What about DRM-wise, or the online components? What about digital purchases for things like the DSi, or Wii games (when that eventually gets shut down)? These don't seem like big things at the moment, since the pickings on there were slim, but it's the precident of those things being lost forever.
The strange position that gaming is in, is that the medium itself changes every half a decade or so (or thereabouts). We went from using a joystick and a single button, to now sometimes you don't need a controller at all. Whereas with PC, it's "here's your keyboard and mouse, go", with consoles the very way that we interact with games alters itself with each progressive generation. Hell, I think this new cycle of consoles is really interesting in that we haven't really seen any significant changes in the controllers. That's nuts.
I know all this sounds like a tangent, but what I'm getting at is that I'm firmly on the side of "have these games for legacy purposes." I get that a lot won't have the space, or even the money (I know I really don't, so I'm a massive hypocrite in that regard at the moment) but like people enjoy having bookshelves of nicely bound versions of classic books, or their vinyl collections, I'd want to have a small part of my house to shelve all my classic games, and while that's easy for the cartridge era, we're moving onto a digital frontier, and like a lot of people and their qualms about technology, I sometimes worry that there really could be the case of "whoop, this game's just gone now! Sorry!" like what happened with MvC2 on XBLA that I bought, but didn't have on my hard drive when it was taken down. So that's just gone forever. And I really don't like that.
tl;dr I think a 'Netflix for games' system would be like a fossil fuel: Great for the short-term, and would probably work just fine, but what about the long-term?