If I open a nfs doc with, let's say Libreoffice, will I not download whole file?

On a second thought, I think you are looking at webdav as sysadmins not as developers. Webdav was designed for document authoring, and you cannot author a document, version it, merge other authors changes, track changes without fully controlling resources. Conceptually is much like git needs a local copy.

I can't imagine how to have an editor editing a file and file is changed at any offset at any time by any unknown agent whitouth any type of orchestration.

Are you saying WebDAV doesn't support range requests?