So you'd like to have your PC running all-day streaming all-day to the LAN, so when you're rdy to watch TV, you have TiVO functionnalities.
The goal is clear. Without a PC. That means you can take your Xbox to your grandfather's house, pause live TV, record it, rewind, etc. without any PC setup. Moreover, you don't need to lose your PC power to do that.
And finally it can be a marketing thing. To sell a fully legal Xbox with PVR capabilities without a PC. You just plug everything and it work. No harassment at all. For PC user it means the same thing. Why is their some specialized Video card? To free CPU from specific calculations. I'd like to see you encoding real-time Xvid and Mp3 for when you want to watch the News, you can go back 5 sec to the healine you missed.