I look at JSX as more of a helper to lower the barrier to entry. In the end it's all just Javascript. You can render the (virtual) DOM in React without using any JSX/HTML syntax. So it's not "everything mixed into HTML", it's "there is no HTML until the top-level render() is instantiated".

Also, regarding the CSS questions, setups like CSS Modules in a Webpack build make the CSS very maintainable. Not to say there aren't drawbacks, but IMO having the classes be dynamic makes everything way more flexible. And, tools like hot-module-reloading make front-end development so much more enjoyable.