I really like using nginx, hosting static files, while also having the flexibility to easily add redirects and rewrite rules, reverse proxy to other apps (and fall back in various ways if that fails), have control over caching, redirect based on browser language, send different image formats based on browser capabilities, etc etc..
Hosting statically would likely be easier for deployment (e.g. essentially zero-effort with GitHub Pages), but with the jenkins-ci.org domain pointing there, it would be less flexible and would require apps (like /account) moving to subdomains. For which we have to run a web server anyway.
There are also loads of redirects and permalinks on jenkins-ci.org, which would be a bit more annoying to implement purely with a static site.
With a static provider like GitHub Pages, you would (likely) also lose to access logs for the main site.