I agree and really like the idea, but I think this feature should be controlled by the user owning(logged in) the Plex server and the option to dis/allow per shared user.
I don't know, I don't really see the use of this feature. Wouldn't you prefer to have sync in desktop clients?
No. Not really. Because the main idea behind this request is to quickly share the original files to a friend... But the Sync feature makes the files only available inside plex