Gaps?

So the Avatar dies, the new one is born, and the cycle continues. The new Avatar's identity is revealed to everyone (except the sages that, in theory, already knew) at the age of 16. So does that not mean then that every cycle, there is 16 years of no Avatar? Like, Kyoshi died, Roku was born, 16 years pass, then begins the Era of Roku. Right? So do we not then regularly have 16 years of unregulated chaos?

I've just finished the Kyoshi books, starting the Yangchen book now, and I haven't watched Korra yet. So if the answer is somewhere in the Yangchen books, the Roku book, or Korra - my apologies. But this thought just occurred to me and I'm really curious now.