Ofcourse you can run Debian on your desktop, but I'm not sure whether that is the main target of an Debian distribution. Many spin-offs of Debian fillful that task.
Another benefit of not running the lastest versions is most bugs are already solved. Debian chooses a version of package for it release and stays there. Only security updates are provided.
BTW: If you really want to run some cutting-edge software on Debian Sarge, you might want to check out the http://backports.org/ website that provide more recent versions of software build for the Sarge distribution.