The view rendering layer is the part that is specific to each platform and the React community provides web components that work natively on each platform making the development process between mobile/web more consistent. Mobile provides an escape hatch to write platform specific code in the native language.
"As for web/ios/android/desktop - this is a rare bird"
Targeting all, will remain very unlikely. Targeting more than one is pretty common. React and Angular2 are pushing hard to enter the mobile development ecosystem. Microsoft has been pushing for Typescript usage on the desktop and just picked up Xamarin so we'll likely see desktop or web or mobile hybrid applications at some point in the future.
If the barrier-of-entry to support another platform is low enough, it'll make sense to do so. In the current ecosystem, supporting even 2 platforms is a massive undertaking.