Kepler's law is an approximation, and it most certainly does not hold over large time scales. Heck, it fails on short time frames too - one of the early successes of relativity was to explain the precession of Mercury's perihelion from Kepler style theory to observation.
Heck, even restricting to classical physics, Kepler's law fails as soon as you have three bodies, since the derivation is only for a two body problem. A third (or more) body makes his laws fail. Our solar system has well over thousands of bodies all interacting.
So this is only an argument for the invariance of the (incomplete) model of Kepler, but fails in real life. We have plenty of better models (i.e., that agree better with observation) that are not invariant.
Kepler's law is an approximation, and it most certainly does not hold over large time scales. Heck, it fails on short time frames too - one of the early successes of relativity was to explain the precession of Mercury's perihelion from Kepler style theory to observation.
Heck, even restricting to classical physics, Kepler's law fails as soon as you have three bodies, since the derivation is only for a two body problem. A third (or more) body makes his laws fail. Our solar system has well over thousands of bodies all interacting.
So this is only an argument for the invariance of the (incomplete) model of Kepler, but fails in real life. We have plenty of better models (i.e., that agree better with observation) that are not invariant.