I am almost certain the Chimera is a Mk 1, but I'm at work and can't immediately check. EDIT Just checked and your right, I'm confusing it with the new continuity where it's a class 1.
Pretty much this, The Empire pretty much had a literal galaxy's worth of material and resources and the main job of its navy was suppressing conflict between planets, policing smugglers and pirates, and other general policing actions since the rebellion lacked anything like a strong or traditional navy. So Star Destroyers are quite literally jack of all trade ships you would send anywhere for anything. Not having it be the flagship itself is a bit much but among his flaws is trouble delegating.