Using --desktop performs multiple functions, including (but maybe not exhaustive) managing different backgrounds for different desktops as well as enabling desktop icons. I want the former but not the latter. The "documentation" (which I've read several times without finding an answer) does not document how to enable different backgrounds on different desktops WITHOUT having the icons show.
My solution, found by trial-and-error, was to set the Desktop directory in my home to 555 perms (i.e., readonly). This works, but is not obvious or clearly documented anywhere.