Then why have a thread about DMOZ at all as I think it's highly irrelevant.
Much like the Yahoo directory is becoming more and more irrelevant as well.
As a matter of fact, the DMOZ directory is SO IRRELEVANT to Google that you'll be hard pressed to find the copy that Google uses as their own directory. It used to be that Google had searching of the directory as an easy to find option, then it moved to "More..." and then it was pushed to the back of the bus on a more obscure page.
Some have tried, and one that springs to mind actually exhibits at PubCon and SES but we're not allowed to mention them by name so I won't.
However, I think the age of the generic mega-directory is over and the niche directories have taken over to provide far better and more customized and personalized services tailored to their individual markets.
If anyone were planning a new mega-directory it would have to be built taking the needs of each niche into account with more to a listing than just a domain name and one line of descriptive text as that's so 90's it's pitiful, which is what DMOZ is, an arcane dinosaur that refuses to evolve.
Will a new competitor arise?
Most likely, but I wouldn't call them a competitor because DMOZ doesn't compete with anyone IMO.
The next generation, if it ever exists, will be Web 2.x-like with community involved and be more of a combination directory, portfolio, lead generation, rating and comparison site that just a mere directory.