Why does a dual-axis autopilot not allow operation in single-axis?
It is neither a design nor regulation limitation. Best explanation I have is that manual control on one axis with the autopilot on another is a bit impractical and goes against normal piloting training techniques. For example banking left/right involves using both ailerons and rudder, but also adding a little bit of pitch up to increase the wing load in the turn.

I used to fly like this a while ago when the pitch axis of one of the autopilots was inop (failed auto-test). It was actually allowed to dispatch (and use the autopilot) but only lateral (HDG/NAV) control was available, with manual pitch. It was uncomfortable to use, counter-intuitive, and we usually just disconnected and flew the thing manually (well, maybe except cruise).