Of course a modern PC can hndle many functions of a home theater receiver. It has audio I/O interfaces as well as video I/O interfaces. At least at first instance it might make sense to use it this way as well.
At second look you will find that a PC is usually not equipped with a powerful amplifier. What you get from a modern sound card are line-out and pre-amped outputs which require external amplifiers as well as some pure digital outputs. I am personally not aware of any HiFi amplifier which is built into a PC directly. Usually you also want to avoid high-power amplifier circuits within a PC as you would also amplify a lot of noise resulting from power surges and many radiation sources within a PC case. This is also the reason why many high-quality sound cards have a metal shield (e.g. refer to Asus Xonar series). This shield is neither for heat dissipation nor just for "coolness factor"; it is shielding the audio circuits from various radiation in order to minimize their impact on analog audio connections.
So given the fact that you either output digital audio signals (which again need an external receiver or amplifier) or analog outputs which also require an amplifier there is not much functionality of a home theater receiver left which you can move to your PC.
Of course a PC still makes a lot of sense in modern home theater systems - but mainly as an A/V source than as the AV receiver. I personally do not own any A/V source except my PC. My graphics card is connected up to my screens and a beamer, my sound card is connected via S/PDIF to my home cinema receiver which powers a high-quality 5.1 sound system. Using the machine I can turn any 2, 4, 5.1, 7.1... stream into a real-time encoded DolbyDigital/DTS bitstream sent via S/PDIF to my receiver. Well, nowadays you would potentially prefer an HDMI connection, but my equipment is in use since about 10 years now.
Windows Media Center also acts as an A/V source rather than as an A/V receiver. Even though you could use a TV card to get pictures from external sources into your PC and display it in media center. But there is still the problem that you need some external speakers and speaker amplifiers.
Given the prices of A/V receivers it does not make much sense to put these functionality into your PC. The functionality is quite "dumb" and static - so there is no benefit of using a complex software system to emulate this functionality. Getting any Logitech 5.1 system (e.g. the Z-5500 is still a good buy for the money) would probably be a much better choice.
Of course one of the drawbacks of an A/V receiver is that its functionality is static. For example such a receiver would just accept a certain amount of audio formats which it's able to decode. Using a PC as a home theater A/V source also helps to overcome some of these limitations. For example my home theater receiver (Yamaha DSP-A1092) only supports DolbyDigital/AC3 and no DTS. But using my PC I can listen to DTS audio sources while my CPU simply decodes DTS and my Xonar soundcard re-encodes it to DolbyDigital Live 5.1 bitstream again so it's accepted by my receiver. Of course usually this is a stupid thing as you decode, re-encode and decode again which is a loss of quality. But some movies are re-mastered in DTS and the resulting quality is still much better than to listen to the original DolbyDigital bitstream as it is on DVD.