In some ways, the title I gave this thread could be construed as suggesting that the histogram should always be full - something which is certainly not the case.
Or is it? Take the example of this image…
… and its histogram…

This was made, quite deliberately, as a high-key image so, understandably, there are very few tones in the first half of the histogram and the image appears as we would expect.
However, if I turn on the over and under exposure warnings, I only have to move the ends of the tone curve sideways by a couple of points…
… and both the under and over exposure warnings start to flash.
Especially surprising for the shadows end but, if you look at this section of the flower…

… in more detail, you find that there are indeed tones that are virtually black, despite the apparent absence of such tones in the histogram. It’s all about the scale of the histogram, where there are simply not enough levels to show such small quantities of a particular tone.
In fact, despite its appearance, I have completely filled this histogram 

