The problem when you use Web Components in JSX is that there is no way to wire up any custom events fired by the Web Component. JSX will only wire up "known events".
That's just when you use custom elements in _React_.
I've definitely wired up JSX createElement implementations that handle attributes and events properly. My preference is for Polymer-style naming: `on-*` for event handlers, `$` suffix for attributes and everything else is a property. Others who've done this use special `attributes` and `events` properties.
https://facebook.github.io/react/docs/web-components.html
There's also more opinionated integrations like https://www.npmjs.com/package/skatejs-react-integration.
And of course you can do it the other way around too.