Money. As the volume of sites on the web exploded, the number of volunteers needed to build a quality directory becomes extreme. Others have not come along to challenge DMOZ because they don’t have the pedigree and reputation to get the necessary number of quality volunteers. (the critical words here being “volunteer” and "quality")
Now, if you’re talking about a monetized directory, with paid editors then that might be an interesting endeavor. However, you won’t make enough to fund it slapping Adsense all over it, and if you charge people to submit their sites that’s a whole different beast.
The real shame in all this is that Google doesn’t provide a few hundred million in funding for DMOZ. Peanuts to pay back to an entity that was crucial to their early existence and development.
All in all an interesting debate because if money was no object, a human edited directory would have a realistic shot at competing with an algorithmic search engine in returning quality results.