You can't make a blanket statement that the cable modem doesn't assign an IP, because some do. Specifically, my Comcast setup uses the system setup with DHCP to dynamically assign the IP to your machine directly from the cable modem. I can pull the line from my router, plug it into my PC, and reboot the modem and do an IPCONFIG /RENEW, and I'm connected directly to the modem.
With that said, some cable accounts want you to assign the IP automatically, but disable DHCP. This was the configuration that I needed for @home, and a specific computer name was also required.
In short, there really is not a single answer to this question.