The choice of a coordinate frame when viewing into or travelling through space depends on what I want to keep invariant (sorry for that word, I'm physicist

Every frame is basically given by two linearly independent vectors (not necessarily orthogonal). Chase mode takes its vectors from two different phenomena concerning a celestial body: the orbit and its own rotation. One frame vector (orbit velocity) is taken from the body's orbit, the other one is its spin vector. I don't see any advantages of this combination.
A more straightforward (imho) setup of a frame, which uses the orbit velocity as a first frame vector, too, could use the normal vector of the orbit plane (= vector of angular momentum) as a second frame vector. So both frame vectors are derived from the same phenomenon, which gives the frame a more fundamental meaning.
If we would watch the Earth's motion (e.g.) in this frame we'd see the Earth's axis 'precede'. In chase mode we see it oscillate in a plane. The motion of background stars in chase mode may be confusing somehow (watch Uranus in this mode!); if we substitute the second axis by the orbit plane normal vector, this makes the background stars rotate smoothly.
I know, coordinate frames are a top issue among Celestia's insiders and therefore will have been discussed widely, including chase mode. I don't want to criticize anything. I only, as always, would like to understand why things are as they are.
lidocorc