Longer answer: The concept of self-play isn't new in any sense. All chess players use this technique to some degree. None use only this technique. The advantage of self play is that there's no risk of accidentally picking up someone else's an incorrect assumption. Since you're deriving everything from scratch. Some people take this to extremes, there's a math professor who doesn't read any math papers so that he's deriving everything from first principles and not "contaminating his mind" it works quite well for him but unfortunately I'm blanking on his name. However, commitment to this technique removes one of the major advantages that humans have which is their ability to communicate knowledge amongst themselves in a compact, abstract way with language. Humans also have a pretty good way to mitigate the faulty assumption risk: skepticism. We can reevaluate our assumptions, and, if we deem it necessary, excise them from our mental model. AlphaZero could in theory do the same thing, the reality for AlphaZero though is that there's not much point, it has no use for the sum total of human knowledge on chess, it's capable of recreating that and much more in a few hours.

If there is something to be learned from AlphaZero's training it's that you should always be skeptical of your assumptions, that's not anything new, but it's always worth reiterating. It's pretty obviously not feasible to take this to the extremes of AlphaZero though, humans need other humans to learn. Even the math professor who doesn't read papers needed a lot of interfacing with other humans to learn to get to the point where he could derive things from first principles.