IMO, static doesn't have to have a correlation to being simpler.

HTML, CSS, JS, and media are all static assets but you're welcome to request whatever datatypes you want behind the scenes via AJAX and/or CORs.

The benefits are entirely in the rendering speeds of an optimized web server and cache layer. Also, this approach plays extremely nicely with CDNs.

Difficulties can arise if you have to begin dealing with versioning of your assets to avoid cache invalidation, but that's what a proper build process can add to the static site.