re: “Radians are just as arbitrary as degrees.”
Oops.
Definition, Radian
Radian describes the plane angle subtended by a circular arc as the length of the arc divided by the radius of the arc.
One radian is the angle subtended at the center of a circle by an arc that is equal in length to the radius of the circle.
There’s no oops there. Do you really think the problem I’m talking about disappears if you use radians? Do you think radians are magical and make the equations work out differently?
Any unit of measurement is intrinsically arbitrary, since we are the ones who assign them (except perhaps for quantum units). The math doesn’t change because you change the unit of measurement.