It would be useful to know something specifically about an axis. Specifically, it would be useful to know the following:
1: What "kind" of axis it is. Is it conceptually a horizontal (X) axis, vertical (Y) axis, a twist (Z) axis, or just a nondescript axis like a throttle that has no true X or Y? This information would be useful for setting up reasonable defaults as well as presenting meaningful names for these controls to the user.
2: The conceptual order of that axis. For example, a PS2 controller has 4 axis controls on it, two X and two Y. Two of these are "primary" axes; these axes are expected to be the most used. Two are "secondary"; these aren't expected to be used as often. Other axes are just additional controls. For a joystick-type with two throttles, the main X,Y axes are the primary axes, and the two throttle axes are just additional axes.
3: Whether certain axes are conceptually grouped. For example, a joystick with a twist has an X, Y, and Z axes, and they are all bound to the same user controller. They are grouped together. That same controller's "throttle" axis is not grouped with the XYZ axes.
I am well aware of the fact that not all underlying APIs provide this information. But for those that do, it would be very helpful to be able to know these things.