Modern computers have limited dedicated hardware in their sound and display systems (and to a lesser extent, in their network interfacing hardware) but none of it can do some of fundamental the stuff that every satellite receiver can do.
8PSK (or even 8VSB) demultiplexing isn't something you can easily pull one element out of by comparing against a local oscillator. It is a complex mathematical task that demands a lot of very fast processing. There are also components to the signal such as error correction that ride on top of the whole package. In the end, there's just too much data that is coming far too fast for a general purpose processor to handle. You're juggling chain saws, marshmallows and live grenades.
There's a reason that nobody is doing a GPS in software. How many radios does that take? Instead we plug in a relatively inexpensive GPS module that sends text data out through a serial port.