Imagine that some Web site collects your serial number in order to finish a transaction. A malicious administrator at that site can turn around and do business with a third person, passing your serial number and claiming to be you. It comes from a program on the impersonator's computer, which is totally under his control. The Intel scheme suffers from many other conceptual problems pointed out by numerous commentators. For instance, people throw out their computers and buy new ones.
Some computers contain multiple processors.
Multiple people also use a single computer. The first component of trust on the Internet is for individual users to be sure the site they've surfed to is what it claims to be, and that it will honor its promises. I believe that the serial number will prove most useful for companies, including Microsoft, that are trying to impose tighter product licensing. And this is a terrible application. But don't get worked up yet.