You may be content with a 10 inch screen, but I live in a flat of 24-28year olds, and my xbox sees more use as a youtube player than it does as a gaming device. My flatmates are content to search for things using the awful controller text input to play them on the tv rather than use the laptops sitting right in front of them. I'd tell them about SmartGlass, but I doubt they'd use it.
Why would they use an xbox for YouTube rather than using a tablet in conjunction with an Apple TV or Chromecast? Is it just because the xbox is already there and always turned on?
Just install YouTube on an android or iOS phone and use the YouTube TV website on your TV...
You can pair your phone to use it as a controller for YouTube TV...