It's not so much desktop integration that's needed at this point. People are stuck all day in their web-browsers--tabbed browsing has basically eliminated the need to use any functionality outside the browser window (e.g. your window manager), and thus discouraged people from using desktop applications, as they now require a greater mental context-shift than just going to the site of a webapp.
Prism has the first, most important step down, and the rest can come later: they push the user out of the browser environment and back onto their own computer's desktop environment. From there, the possibilities are (for now) simply greater.
Prism is nice and open, however, and combines well with any web technology that works in Gecko. That includes XUL, SVG and scripting, which gets you pretty far with developing desktop apps.
AIR and Silverlight both dig deeper into the desktop, while not as deep as a tradition client-side app, but deep enough to do interesting things.