I think it's probably a combination of things. In the Richardson footage, he does look like a phenom athletically but a completely different fighter. I imagine he transformed as he got older into the Moore we see against Johnson, Bivins, Marciano, etc I also find it likely, given how well rounded he was that he changed how he fought for his opponents often, and that likely kept him winning when he shouldn't and you here's also a possibility that he avoided a lot of the wear and tear you'd get fighting as often as he did. I suppose you can take it easy against guys who don't have much of a chance, knowing he can set up the KO. That type of attitude would explain a lot of his losses too. Like most fighters, he seemed to lose athleticism as he got older, but the added experience contributed to his rising ring IQ. He likely lost a lot less athleticism than most due to genetics or training, and his ring IQ also got higher at a disproportionate rate.
Don't have the source off the top of my head but Moore used to do a lot of training that worked his balancing and proprioception abilities. He was big on walking on his hands ala Lomachenko. Supposedly he would even do it up steps as a younger man. He was also very stringent in shadowboxing in front of a mirror to correct his form and notice his tension. Would apparently shadowbox with his eyes closed sometimes, too. Seemed like he did a lot of training that really encouraged his mind-body connection beyond just mindless conditioning work.
Yeah, Usyk is a great example of this. Always surprises me how many Boxers simply don't do it at all, especially at heavier weights.