React was first at DOM library that introduces virtual DOM based solution for "Components". And it's very to have component level state called local state that is attached to a component.
However global state is not that simple. As I can see, that Store is sometimes a clone of a subset of the database, and sometimes it's global component state, and sometimes it's app state. It's quite like a mixture and there quite a lot scenarios. It's not that simple. Even Facebook release Flux trying to fix that. It's not good enough. And people also want Redux or Mobx or something else. It's just too complicated to finish in React itself.
Since I'm a ClojureScript user and I also seeing this case from another side that JavaScript is not clear enough about mutations and immutable data. With such functional concepts there are not many choices left so the answer looks much simpler. While in JavaScript, people want a lot.