I don't think this idea is correct, but sharing it because I thought it might be interesting.
I recently read that the average child is less evolutionarily fit than their parents, but this is fine because the ones that are more fit will go on to have more children, and so the ratchet of evolution can continue to turn. I can't remember exactly where I read it—I thought it was Dynomight but it seems not to have been, but I think it's just a normal understanding of evolution.
If that's true, then could it be the case that the Illusion of Moral Decline is actually driven by this effect? Because non-reproducing people don't feature in anyone's ancestry, and are by construction less evolutionarily fit, then looking back across your family tree you should broadly see an improving or at least stable fitness, which should be higher than the average person alive today. So at any given time it might be possible to say 'this generation is worse than all the generations who have come before'.
I don't think this actually works because it's attempting to bundle evolutionary fitness and moral quality in ways that are not necessarily linked. But it gives a reason to violate the Cosmological principle for 'the current generation', marking it out as specially different from any other generation (or the view that we have of any other generation).