The most compelling reason for building a static version of your React components is to provide a better experience for your users. The key metric here is the overall performance improvements. Instead of having to touch various API endpoints and handle all of the asynchronous aspects of providing data to your React components, everything is loaded upfront.
Another less obvious user experience improvement with statically built React content is that since there are fewer moving parts, there's less chance of the site breaking, leading to user frustration. For example, if your React components don't have to reach out over the network to fetch data, this failure vector is removed entirely from your site.