After all, most sites out there probably don't need server-side dynamic preprocessing for every request. The CMS directory could be locked using HTTP auth (implemented by the HTTP server); this way, not every little CMS bug would allow the world to compromise the whole server.
Do we really expect every parish choir with a web site to hire a CMS specialist who installs updates within hours of the release and fixes all compatibility quirks that occur with new major releases? This is an unworldly approach that bestows thousands of zombie machines on us.
And what happens if the CMS for some old site stops being maintained? A responsible admin would shut the site down, resulting in a loss of potentially valuable information. This issue would be solved by using static HTML export, too.
Are there any well-maintained open-source CMS out there where static HTML export is an integral part of the architecture, ideally with good usability and written in PHP (not that I like the language, but that's what is available everywhere)? (I'm not talking about command line static site generators without a user-friendly backend - those are only an option for techies.)