One big advantage to serving static pages is not having to worry about security in the same way.
The core of my project - the thing I consider most important - is the databases (and the code to generate the webpages). Since neither of those is ever accessible on the internet, my security concerns are minimal.
Plus, the website itself if just serving static HTML files - so no need for all of the fancier extensions that include so many bugs and constant updates.
Another advantage is disaster recovery. I can have my site up and running on pretty much any flavor of server in a matter of hours - just have to upload the files.
If I had to recreate the site from scratch, I could do it within a day (as long as the databases and code is intact).
(Needless to say, I backup the databases and code frequently :-)