That's kind of what the UK's Project Canvas was supposed to do. TV guide entries and on-demand catalogue entries both point to the same object in the database, so if you try to watch a show or movie that's not currently airing, it quietly redirects you to the appropriate streaming service instead. When you throw IPTV support into the mix you suddenly have a platform where there's no functional difference between content coming off the web, HDD, or airwaves, recorded or live. From that it's a short hop to a situation where every streaming content provider is offering up its wares (ad-supported) to the same audience and it's all consolidated in one place.
Of course with no generic live IPTV broadcasts in the UK, what happened is that each communications company built their own live IPTV silo that only their subscribers could use, and chased after exclusivity deals on streaming providers. Ultimately all that happened is that communications companies got the broadcasters and the licence payer (including the BBC) to fund their set top box R&D. Admittedly this raised the standard of set top boxes considerably because they were total garbage.
Microsoft tried a similar integrated interface thing for the Xbox 360, where one search box could take you to whatever streaming providers sold what you were looking for. The same interface would also have live IPTV. I don't know about the rest of the world, but in the UK most of the streaming apps just plain don't show up in it. The IPTV functions didn't appear at all.