"It is usually desirable to have a full histogram because it typically means you have a well exposed image with a wide range of tonality present."

That is not entirely true. A low contrast scene will never have a full histogram no matter how you expose it. The spike can be at the left end, in the middle, or at the right end depending on how you expose it, but it will never extend from left to right, and it still can be correctly exposed. You perhaps can boost the contrast up in the camera or in post processing set the black and white points to extend the histogram, but it won't look like the scene you started with.

Alan