To understand the magic behind it, google "hard links." They are references that point to where the actual data resides on the disk. A hard link to a file looks exactly like the original file (because it is).
Except for special circumstances, all files stored on iCloud Drive have copies stored on your Mac in your user Library/Mobile Documents/ folder. This folder holds the files you drag into iCloud Drive or files stored in iCloud Drive from a mobile device.
Your Desktop and Documents folders currently still exist where they were, along with all the contents.
When you disable Desktop & Documents in iCloud Drive, hard link of all the files will be moved to iCloud Drive's backing store location.
When you drag them from the iCloud Drive folders, hard links are moved back into your now empty home folder Desktop and Documents folders. Nothing is actually moved on disk.
iCloud Drive is just a place on the internet where you can store files so you have access to them from some other device. If you don't have any other devices, or you don't intend to need access to a file from your local Library or other internet café, then you don't need iCloud Drive enabled at all.
Although this is a System Preference, the users (other than Admin (me)) have local Documents and Desktop folders that show up in Finder. What am I missing?
It is a system preference for a per-user feature. Each other user would have to sign into their iCloud account and enable the feature.
The feature was enabled for you because you skipped through the setup assistant without reading the pages. It told you it was going to enable Desktop & Documents in iCloud Drive and was defaulted to on. You could have disabled the feature before it was implemented, just like your other users.