I would say that the biggest headache for the computer is what was specifically omitted from the original request in that noise from the PC in the analog realm is typically pretty bad and that is what the best sound cards with external DACs are made to avoid.
Still, the PC can do everything in the digital realm and typically can do so very well. They can be upgraded to handle most of the audio codecs on the market just fine.
The question really becomes - why?
Audio codecs don't actually change that often and a good deal of what we've seen in the past few years with HD audio had been because of Blu-ray and the HDMI chip sets being changed to handle the higher bit rates which were required. It wasn't a software/firmware upgrade, but an actual physical upgrade which was required.
Still, HD audio has been around for a number of years and it is not the audio which has changed as much as the container it is in. DVD-A, SACD, and now HD audio on Blu-ray. But, the quality of the music is often the same, or very close. The PC can handle all of those flavors, if you have the drive to play them back, or get them into your computer as lossless, and you have a good sound card to deal with everything, and the know how to do it all.
Forget theory, people are doing this all the time!
Still more though are not. Instead, they go out and buy a $200ish Blu-ray player, drop a disc in, and play it back. The PS3, from four years ago now (?) is able to handle all of that just fine.
But, if you are looking to source HD audio from the Internet, which does exist, then you likely will be wanting a good sound card to do it all, and for that money, a dedicated HD audio player may offer a more friendly end user experience.
There is no snake oil here, and a simple sound card in your $1,000 computer, will do a very good job. That's $1,000, and you still need the A/V receiver to decode from PCM uncompressed to the amplifier section and volume control and speakers. Plus, the kids may be using the computer right now.
Many people run a dedicated HTPC, and this is pretty much exactly what you are talking about the end result being. A dedicated PC, with HD audio capabilities and a good digital or analog output section to deliver quality audio to your home system. The price is rarely inexpensive on this, but it isn't out of the water either.
Yet, it's important to realize that at some point the logic of running things will exceed the capabilities of the PC. A five year old computer may be able to decode H.264 video, for example, but it can't do it fast enough for smooth real time playback. With audio, this isn't as big of an issue, but the potential certainly is there for this to occur.
It's also notable that newer A/V receivers, have an Internet connection and perform on the fly firmware updates which may enable additional features which did not come originally with the product. I think this will be standard inside of ten years or so and we will see audio chips which allow for firmware updates which can handle new formats when they come to market. Not sure what new audio formats we will see, but most likely it will be about new compression formats to make things more easily downloaded at higher quality.