Static sites for large institutions is asking for trouble down the road.
Think about universities with hundreds of content providers. They'll put anything and everything on their sites with no regard for the standard layout/design. CMS gives them design choices, and enforces standards so you can update/refresh the look and feel in the future.
It's an easy distinction: if non-programmers are managing the content of the site, don't use a static site or a static site generator.
Asking people whose job isn't "building websites" to edit text files, run some sort of compiler on the command line, connect to a server via FTP, or deal with version control is a total failure mode.
But if a developer (or an especially adventurous designer) is going to be editing the content of the site as time goes on, then static files or a static site generator can be a great option.
