In general the React approach works best if you are willing to build out a handful of utilities on your own sometimes, rather than always choosing from pre-existing open-source solutions. You don't need React Router. You don't need React-Redux. Heck, you don't always need Redux, you can just throw a state object on the window (or make a state module or whatever you do these days).
Here's a React 15 app in a single HTML file, using ES5 and the old in-browser JSXTransformer:
https://gist.github.com/guscost/27736c5f0913184695492ac40fd3...