It's been tried. IBM is one company that tried to put only the parts the user needed on the desk (in an all-in-one style display) and the processor and hard drive under the desk. People just weren't interested, and it was clunky.
One reason you can't do what you want is the signals and speed. In order to have the optical drives separate from the mainboard, you'd need to use USB or Firewire connections, or maybe eSATA. In either case, distance becomes an issue. Video signal is also a huge issue, as high resolution and refresh rates require a good signal, and shorter cables. I think DVI allows for longer cables though, since it's digital. There are also of course USB "video cards" that let you plug a VGA monitor into a USB port, but I think their resolution/refresh is very limited, and quality probably isn't great.
Another reason is the fact that you'd have to route these USB and video and keyboard and mouse cables through your house somehow. Do you really want to have your PC permanently stuck in the one corner where you put the connections when you ran them up the wall to the attic and over to the closet? Or have cables stretched across the room under the carpet?
In order to mitigate some of that, you could come up with some sort of single cable device where the desktop components plug in, a single cable carries the data back to the PC. But that'd be a thick cable, since you can't really do anything to the different types of data signal to combine them into one. Anything that would be effective would be expensive and proprietary, and take a lot of development.
Most people who are looking for screaming fast systems aren't that concerned with the noise, or are able to tweak it to make it less loud with better fans and the like. Regular users might just have a system stuck in a desk enclosure that muffles it anyway, but they're also the ones who buy pre-built systems that are quiet from the start, even if they're fast.
Depending on where you have the machine, you could just stick it in a closet, 10 feet of cabling is easily doable, using USB optical drives and extensions for keyboard/mouse, or just a USB hub and cable. Video cables at 10 feet are no problem. But then you have to make sure that closet is ventilated too, since that noisy system is so loud because it needs lots of cooling.
Or you could learn to knit and make a "computer cozy" to muffle the noise. 🙂
