Yeah, it offers little real benefit, with significant extra effort.
1. If you want to support browsers on mobile phones, text-based browsers, disabled users who need assistive devices, or users who prefer to navigate using the keyboard, you’d need to use regular old links/buttons with click enabled anyway, and then layer the don’t-click mouseover stuff on top of that. So first you’d make your site work the traditional way, and then do a bunch more work to enable don’t-click navigation, just to.. accomplish what, exactly? Impress a few people maybe? (But also probably annoy them.. see below.)
2. DHTML has only recently become powerful enough to smoothly present transitions the way dontclick.it does natively. So in the past, using their navigation style would mean making your whole site in Flash – which has it’s own set of downsides (e.g. getting yourself indexed by search engines is much harder), plus is harder to code, or at least requires a significantly different set of skills than traditional web development.
3. In order to make the experience as smooth as dontclick.it has done, you’d need to get away from page-to-page navigation for transitions in content, and move to showing/hiding information that’s either dynamically loaded (which could be jerky on a slow connection) or preloaded (in which case you have to load a huge portion of your site on each user’s first hit). And then how would you support the browser’s bookmarking function for particular sections of data? Yuck.
4. It’s annoying anyway, because if happen to sweep your mouse across the page to accomplish some unrelated task (e.g. to click a program in the dock), you accidentally trigger navigation.