Spine covers.

I don't know. I don't like them myself. But I think a spine cover is by definition still a cover

Can you give examples of what you refer? Is this under cover flagging or what?

Under cover flagging, yes : https://www.librarything.com/helpers_covers.php

Yes, I don't flag those. Tough flagging really does not nothing one way or another. I don't think t even pushes flagged ones to the bottom