staff text

I believe the point of staff text is that it stays with the staff that it's assigned to, so it doesn't copy/paste to a different staff with the music. What you can do is click once on the staff text, copy it, then click on the note you want to assign it to on the new staff, and paste it. This method is quick if you want to assign the same staff text to multiple lines. Copy it, click a note, paste, click another note, paste, etc.

If you want some particular text item to appear on all staves, use System Text rather than Staff Text.

That said, there are certainly plenty of situations you you might want text to copy for other reasons - like a text marking that should only appear on certain staves, or if you are reusing a section later in the piece. I too would very much like to see the ability have staff text and other items copy (and to force certain items that currently copy, like chord syumbols, *not* copy). Ability to control what gets copied is definitely something the developers know would be useful; it just hasn't made the cut yet.