Yeah, a modded Xbox is pretty great. An unmodded Xbox is pretty shit. Emulation isn't %100 perfect by any means, but it excels at CPS2, Neo Geo, older arcade games, Mega Drive, and even does a pretty great job with SNES, although the sound isn't perfect, only a really really picky person can tell.
Yeah. Except it's weak. And not a PC. Why not use a PC instead?
Several reasons: The video output of an XBox is better than a lot of PCs if you are playing on a TV. Xbox machines basically suck for all but about 4 actual Xbox games, which makes the actual machine extremely cheap. You can get one for $60-80 if you are lucky. Pretty hard to build a computer for that. It doesn't run Windows, so you can just use pre-prepared HD images from BT or whereever and be up and running rather quickly with no wierd dll issues, or driver problems, or whatever. If something gets wacked, just copy the same image over again and your good as new. Xboxes make pretty good DiVX players too.