A have a CX bike and I will never get rid of it . . . unless I replace it with a nicer CX bike.
I started out with a road bike and a mountain bike for my commute, switching between them based on the weather, but now I am down to a single CX because it does EVERYTHING. It has the benefits of speed when I put my road tires on it (it's faster than my road bike I sold). In the winter I can put on stubbies and it rides wonderfully in the snow AND ICE (I have never slipped on my CX, which is more than I can say for my mountain bike, but I have some great tires on it). In summary, they're almost as fast as road bikes, but they're built to withstand dirt, grass, gravel, snow, and . . . pavement. Cross bikes fit racks and panniers just fine, so they can even be used for touring if you want. They are incredibly versatile bikes and great for the commute!