This is so true. Just apply the Redux idea of smart/dumb components but without actually using Redux. Higher level component(s) becomes smart and handles the state changes while passing down only properties to children.

Usually I start an app like this and when things get really complicated I add Redux and refactor the state management out of my top component.

MobX looks interesting, however didn't get to try it out yet, only briefly looked over it. I find it a bit annoying that they introduce even more syntax overloading - annotations - as if ES6/7/JSX is not enough already. Will give it a try on a pet project soon.