Earlier quoted context omitted.
Then you aren't benefiting from React at all. The point of React is DOM diffing, which you trigger using setState method.
When you change the props of a component it re-renders. Just because you use pure functions doesn't mean you don't get DOM diffing, that's silly.
But the very fact that we're having this debate is proving my point. React's programming model is unnecessarily complicated. JavaScript + DOM is all you need. The simple libs (each less than 500 lines) I pointed to get you close to this without sacrificing productivity or code maintainability while keeping the programming model simple.