The man page for cpio sez:

     --quiet
             Suppress unnecessary messages.

yet despite using this option, when I am using the -l option (to make sure
that hard links are used, when possible, on the destination volume) I am
still getting lots and lots of annoying warnings like:

Can't create '/my/path/name': Cross-device link
cpio: Copying file instead

These errors & warnings are clearly "unnecessary" in every sense, because
after all, the file _did_ get copied.  It just was not created at the
destination as a hard link to the original source file.

So given that these meessages are really and truly "unnecessary", according
to the documentation (man page) of cpio, the --quiet option should suppress
them, but it doesn't.

Fix: 

Dunno.  I haven't looked at the code, but it ought to be pretty simple.

This is like the old doctor joke...

Patient: "Doctor!  Doctor!  It hurts when I do this!"

Doctor:  "Don't do that!"

It ought to be pretty simple to just NOT produce these unnecessary messages
when --quiet is in effect.
How-To-Repeat: 
Try using the -l option and the -quiet options together as you use cpio to
copy a file from one filesystem onto another different one.