It is common knowledge that of the classical tests of GR, gravitational redshift is normally considered to be testing the Equivalence principle and conservation of energy rather than the full GR theory. So it is considered a more fundamental test of our basic principles of GR and physics in general. Actually in some GR books it's stressed that what gravitational redshift experiments prove is E=hf (planck equation) when energy is conserved. But at the same time it is claimed that energy conservation in GR doesn't apply to cosmology, does this mean that gravitational redshift doesn't apply to cosmological distances? Let's imagine a supermassive Black Hole with an event horizon radius of cosmological size, would there be no gravitational redshift in that case?