Chromecast seems to be a method for driving-devices to send pointers to internet video streams or web pages, for the dongle to queue, download and then send to the display. The apps/content don't live on the mobile device at all. They live on remote internet servers. The device is just feeding a queue.
I'd also add a wrinkle to your statement about devices being awesome as typing/searching interfaces: that's true, but they come with negatives.
The real problem with "device as brains", is that your device does many other jobs. And you may not want those jobs in-your-face when you're watching a movie, or showing pictures, or even just trying to add background-music to a dinner party.
Devices are more difficult to deal with when you just want to pause something, the notifications are there, the temptations are there and the social negatives are there [1].
But while everyone's tossing out Airplay wish-lists -- it'd be nice if I could airplay a movie to my TV but have the audio still piped to the headphones.
[1] You may be trying to switch playlists, but to everyone else it looks for all the world like texting.