At the time the Video Toaster was not a finished product and the Amiga's video output was never fully broadcast quality, mainly because the display didn't cover the entire width of the screen. The setup used on CC involved Targa graphics cards and their RGB outputs were externally encoded to NTSC using Faroujda encoders and then somehow genlocked. In addition, a custom-built control panel was attached to these computers to control the whole affair. I also seem to recall that hard drives for the Amiga in those days were not quite commonplace.
Playing a home game, if the computer hiccups it's "Oh, well." In a live network television production environment where downtime costs by the minute, you need a more "industrial strength" solution than plastic-cased Amigas. They say that nobody ever got fired for buying IBM, and when you have a $20,000 budget, why go with a $500 consumer-grade computer?
As for using two PCs, I don't know. Corey Cooper could tell you why.