Most devs I know start a react application by cloning some standard git repo which has a working webpack/tidyCSS/redux/some test suite etc. and then write your first line of useful code. The boilerplate is enormous!
As for build systems vs. script includes... I think Vue is probably being used in a lot more hobby projects than npm downloads would seem to indicate...but using a build system is a stronger indicator of a professional web app and pretty much necessary for any non-trivial project.
Edit: more information: https://github.com/babel/babel-standalone/blob/master/README...
It's /really/ not intended for use in prod.
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Edit. I kinda sent off on a stream of conciseness about reactjs.net here, feel free to ignore this bit.... :D
Infact, as well made as it is and despite using reactjs.net heavily for the last couple of years, the only time i would be inclined to use it on a new app is to leverage the universal rendering, or if your react app is just freaking massive and takes forever to run a build - otherwise you may aswell just throw everything at webpack --watch via iisnode or regular 'ole vanilla node.
Then again we had to make a bunch of changes to the package itself to fully support our bundling (we don't like cassette so we made our own) and to support multiple server-side bundles, none of which are agnostic enough to warrant a PR, so upgrading reactjs.net to a more recent version is a hassle, making me slightly biased against using it ;)
<div id='root'></div>
<script src='https://cdnjs.cloudflare.com/ajax/libs/react/15.6.1/react.js'></script>
<script src='https://cdnjs.cloudflare.com/ajax/libs/react/15.6.1/react-dom.js'></script>
<script src='https://cdnjs.cloudflare.com/ajax/libs/babel-core/5.8.38/browser.min.js'></script>
<script type='text/babel'>
const App = () => <div>Hello World</div>;
ReactDOM.render(<App />, document.getElementById('root'))
</script> elem.div(elem(Component, {prop: 'value'}), {className: 'foo'})