This is a design limitation of the Animation palette. If you pick copy off the Edit menu it copies the current body part, not the entire frame. So, just the head or hip or whatever is selected in the pose window. The keyboard method is the only way to copy multiple frames. But, there's another keyboard trick which is much faster for making loops like walk cycles ...

Select the range of keys you want to duplicate. Then [Alt]+Drag them to the new location on the palette. Drop them where you want to loop your animation. Copied and pasted in one action.