Okay, let me clarify a bit after having toyed with it a little more. Firstly, I think the two current modes offered are good to have as is. These shouldn't be changed, as they are useful for various specific application as has been mentioned. (Its good to know that these were done intentionally and are not a limitation of the Blender 3D space.)
I would only request that another mode be offered that adds the "twist" (or rotation along the view's axis) to the turntable mode. This mode is good in that the "pivot point" of the view is somewhere other than the view's (or camera's) centerpoint itself. Thus the object upon which the view is focused remains centered as you rotate the view. (But moves as you pan the view - panning moves the pivot point.)
It would be nice to have a button or command that allowed you to "recenter" the view at a user-defined point, be that the currently selected object or vertex, the 3D cursor, or whatever (several options would be good here.) This should be available for both turntable mode and the additional mode that I'm requesting. For fly mode this wouldn't necessarily apply, tho for transform mode it might be handy as well, defining the point at which the rotation transform is centered.
Steve F wrote:When you say other apps have the full 6 degrees are all concurrently available, how is that different than fly mode?
As I've mentioned above (and hopefully to clarify) in 3D CAD apps this is different from Blender's fly mode in that the pivot point of the view is somewhere other than the viewport's own center point. Think of the view as a camera. Fly mode rotates the view around the camera's centerpoint, allowing the user to "look around" so to speak (how your own head works

.) Turntable mode assigns another rotational centerpoint, usually centered on the object of interest (some geometry that's being viewed) allowing you to kind of "orbit" an object while keeping it centered in your view.
The difference between Blender's turntable mode and your typical (3D) CAD mode is that in Blender they appear to have disabled the rotation around the axis of view (I think) where in CAD all 6 degrees are avialable in combination with an assignable center of interest (rotational centerpoint). Its this functionality that I'd like to see added as another "mode".