One of the big reasons I lean toward static sites for my stuff is that you can host them out of an S3 bucket or similar with no dynamic endpoints whatsoever. This is a huge win for security for projects that I don't have time to keep constantly updating. A web-based admin backend largely eliminates that value unless it's run off a separate port that I can firewall, and even then I have to be sure I firewalled it correctly.
There is a space that I'd like to explore, though, and that's having a static site generator that is built into a desktop-based GUI. My dream is to get the brain-dead security of an SSG without having to fiddle about with files and folder structures.