Doug, I would tend to agree with your statement regarding depth, as it is something I often struggle with when composing but never really realized until recently. Depth highlighted or leveraged is what actually makes many photographs work, irrespective of the processing or other aspects of the composition. Understanding DOF appears to only be a start, as the rest is imagination and understanding how the DOF will affect the actual composition. I suppose the camera is no different than a paintbrush or any other tool, it takes talent, imagination and practice to master.
This is truer than you realize. Having in focus items in the foreground help to show the depth of the image. They should also tend to lead the eye to the central point of interest. Having the out of focus item won't show the depth. It can also be distracting. It does help show the point of interest when an object is not removable though. It may distract some, but the eye still goes to the focused part of the image.
I have a 77mm Nikon CP you can play with for a while if you'd like. At the cost of some lenses, it seems expensive, but you'll see the difference if comparing it to a 50 buck CP.