I can create a chat application in just ruby, that stores everything in a flat text file and serves everything directly from mongrel, with no apache or nginx in the way.
Just because it has "fewer moving parts" doesn't make it good or special.
Separating unrelated layers is supposed to be a good thing. I seriously doubt that CouchDB is as good a general purpose HTTP server as Apache.
UPDATE:
This is what I think of when you say "It's got one less moving part":
First thing comes to mind is CouchDB should not be general purpose HTTP server.
You will agree that you can't create real time chat in under 100 lines of Ruby code alone (still you need javascript)
This chat application author coded application in 100 lines of Javascript including validation that run on server.
I can clearly see the benefits of approach CouchDB took with CouchApps. I also know its not answer to all needs of Webapps.