I think the great think about React, and stop me if I've missed your point, is that they're actually just libraries, not framework's, you can just pull in the parts you need and work off of those.
Say you're just doing a single page application, with some basic logic. You can just use React on its own to create components, as you don't need an entire state life-cycle. We do this a lot to 'enhance' our statically generated sites.
Or completely on the other end of the spectrum, you can use Redux, isomorphic rendering with Nodejs for example, react-router, and you can create a complete, dynamic site, with state, storage, authentication, whatever you need.
Then you have everything in between.
So you really can use React "for everything" in my view, and that's partly why I love it so much.
I don't think React is just an "evolution of template libraries", I think React is a concept, I know React didn't invent this concept of 'components', far from it, but I think it brought about the most clear-cut, concise way of creating web components, largely thanks to React's use of JSX, I think. When you team that up with Webpack (which you totally should btw), you can house all of that components dependencies in the same directory, and call them within the component, a truly modular approach.
(I promise you I don't secretly work for Facebook, I just love React).