I don't quite agree with your definitions of cover and case, though I understand what you're talking about.
My Sony PRS-T1 has a
silicone skin and has a
CaseLogic hard-sided zipper case, but is only in the case when I'm transporting it. However, my T1 is relegated to being my "home machine" (like my desktop computer) now that I have my Kobo Mini.
My Kobo Mini has a
beautiful leather cover (case? It's surrounded on all sides and extends about 1/8" past the ereader so all edges are protected, but doesn't have a zipper).
Given the size and weight of my T1, I really like to read with it only in its silicone skin (no cover). However, the Kobo Mini is so small and light I don't mind the cover (and the leather feels really nice to hold).