You mean Rhino’s XYZ system? It’s not arbitrary, it’s a standard.

I don’t understand why you have to go back if you don’t need it.

Correct me if I’m wrong, but all the ortho-normal base changes you refer to, going from global G{x,y,z} to local L{x,y,z}, or vice versa, are actually L = T(G) or G = T’(L), where T is an orient type transformation (moves from this origin to this other origin, rotates from this X axis to this other X axis, this Y axis to this other Y axis, and so on). Rhino can’t escape the XYZ standard, and you can already create oriented points as David suggested, I agree it would be nice to include the vector version btw. With my previous answer I meant that it is the same vector space but with a transformation, and to include that in a point constructor is what Point Oriented does.

Think that you take the definition of another person, and move a point, you see the coordinates of the direction of movement and you do not fit with the global XYZ result, you, that you know, can deduct that the base plane parameter has been changed, someone who does not know about vectors (which are many that start in GH and do not have an architectural background for example) will not understand what happens with the simplest operation of all, moving a point, until he/she understands some of vectorial algebra, I don’t see it as a rational problem, I see it as an emotional problem. GH already fails a lot in this sense.

On the other hand, if you keep it as it is, or use the specific components for it, or apply the transformation in another way, it is something that leaves a visual record in the definition at least. There is no need to modify these components, other can be created.