Your Chromecast takes 30 seconds to load content? In our house someone pretty much always has either their phone, tablet, or laptop nearby and with the HDMI-CEC, you don't even have to find the TV remote to switch inputs, you just queue up want you to want to watch and it plays. And then people can take turns with their respective devices (if you're watching YouTube videos or playing music, etc.)
We also have a Roku and used that before the Chromecast, but the Chromecast is more popular with everyone (kids) in the house for the aforementioned reason of communal use. It's like the Nexus Q was supposed to be, but for video.
So I got my Fire TV. It has some CEC support because it shows up as a source to my TV and the TV and receiver correctly switch to it. My TV remote, however, does not control the Fire TV. Given that the HDMI hardware supports CEC, I think this was their choice and one that they hopefully will change with a software update.
We also have a Roku and used that before the Chromecast, but the Chromecast is more popular with everyone (kids) in the house for the aforementioned reason of communal use. It's like the Nexus Q was supposed to be, but for video.