What exactly is the role of a "media box" (WD Live?) here? Why not straight from PC to Receiver/TV?
1. If your PC is in different room from the TV it may not be convenient to lay a monitor cable.
2. You might not want a big or noisy or unnattractive PC in the room where the TV is.
3. You might not want a Windows desktop on your TV.
4. Your PC's media server of choice might not have as elegant a 10' interface as a media box and it may be more complicated to get working and to remotely control.
5. If you have a low-spec PC, video might be unreliable.
6. Your PC might not have the video/audio outputs that you require.
7. If you have several rooms, it will be cheaper and maybe more convenient to put media streamers there instead of a HTPC for each room.
8. "Media box" also includes TVs and BR players that are DLNA DMRs, so cutting out the middle man - straight from PC to TV as you've stated but via ethernet rather than HDMI, as long as you've got network in your TV room.
I'm sure there are other reasons that people may have!
Will this help with 1080 video that gets choppy in MC?
That's something I don't understand. How come all cheap streamers can handle HD video yet it takes a pretty powerful PC to do it? It took a lot of tweaking to get my MC to do good video (and I'm still not exactly sure what I did) yet the WD TV Live does it straight out of the box.
Can I run my desktop through this so I can use my HDTV as my desktop monitor?
I don't think so. There is actually a UPnP protocol that allows a server to "project" an application interface to the device but I'm not sure if anything has implemented this as yet. There may be a piece of software that can capture the desktop and broadcast it via DLNA but I don't know, I think companies like Hauppauge and DVBLink are the likely candidates for something like this if there has been anything developed.