Heard of these guys
? I haven't tried their stuff, it isn't cheap, but it does seem to distribute HDMI all over Ethernet. The biggest plus of this system is it is basically an infinite matrix switch limited only by the port capacities of your network of managed routers. The other benefit is you can have sources anywhere, just connect them to a transmitter box. Need another source, buy another transmitter, install it next to the source, connect it to the managed Ethernet network. Need another sink, buy another receiver, connect it to the network, connect it to your TV/receiver/whatever. They also mention you can do an "audio extract", so 2 channel zones are supported, too.
That said, I do believe you're very right, it seems there is no company really looking to fully integrate a user's audio/video library, with live/recorded TV, streaming, and any HDMI-based sources. Of course, that's probably because the market for that level of integration is smaller than the cost to fully develop it. However, since most of that stuff is done over Ethernet, maybe just putting the HDMI sources on Ethernet as well could be one more step to more easily integrating stuff.... "One cable to control them all" if you will, lol.
Good luck! I know I, too, was frustrated when I wanted a one-stop shopping solution forever ago. I just gave up, deciding that while it would be really neat to have all that, it was just my wife and I plus an occasional guest in our home, and we didn't need to appropriate money to something we'd never use to its fullest extent.