What if you count rotation around the vertical axis? I have a kensington trackball where that is how you scroll.

Then you can no longer rotate, unless you make it rotate when you push some additional button. The 3DConnexion devices have 6 degrees of freedom without pushing any additional buttons. That being said I have a SpaceNavigator and I don’t use it, it’s just sitting in a drawer and I use my regular mouse and keyboard even in Blender.