From what I remember, it's pretty chatty. It appears to be on its way out. Is there any new software that's using it?
WebDAV had some varying levels of support in Windows and Mac desktops. But AFAIK the Windows stuff got broken; not sure about Mac. I think that access from a GUI file browser was one of its main use cases in the 90's. If nobody does that anymore, and I don't think they do, then the protocol will need a new app or it will continue to die.
I've used it to bolt file storage on a REST API for enterprise stuff. It seems to be a good fit. I'm even using the Windows WebDAV implementation... working around its quirks is madness: http://www.greenbytes.de/tech/webdav/webdav-redirector-list.... Note that XP SP3 has the port-handling bug even though it's not on that list.