If we are just talking about DP, directories are important and we all know why, don't we To me, DP is the forum where "directory" is the most talked subject...
You got it right, we depend on search engines, they dont depend on us. I think the OP must surely have been asking that question tongue in cheek?
Did someone mentioned the free backlinks from siggy's and posts that we do here? ah Webmasters are greedy!!! LINK Hunger can never be fed!
Directories do not necessarily or entirely depend on Search engines, Search engines do not entirely depend on directories, however access to the contents of quality , human edited, directories is beneficial to SE's, afterall we do their work for them, at no cost to them, editing , reviewing websites, Ergo, it is always in the interest of se's to promote good directories an to discourage bad directories, It is a symbiotic relationship
Until they are very well established it pretty much is the case they rely on search engines, even if it is via the indirect route.