Microsoft kinda broke WebDAV by adding various incompatible extensions and building a horribly broken client into Windows.
When users found out about all the issues, they preferred sticking to the old FTP, having a desktop sync app (eg. Google Drive), or using a WebUI for managing files (eg. Dropbox's website) etc.
Because SFTP is a better fit for simple (but secure) file transfer, WebDAV handles a lot more, but it's overkill for most of the things FTP was used for.
OTOH, AFAICT, SFTP has largely replaced FTP for the system-to-system role (though ad hoc HTTP-based protocols are also common.)
For me I've always found WebDAV to my owncloud server from Windows and Mac dreadfully slow. The sync client itself that uses WebDAV is just fine, so I'd put my guess on poor integration and client implementations.