I kind of disagree with the OP for a few reason:
> You can’t update your website unless you’re at your computer where the static site generator software is installed
We use svn/git post-commit hooks for this. The generation is done server-side.
> You can’t have local comments, pingbacks, non-google site wide search, contact us forms (without some dynamic code etc)
True, but for example, we have some dynamic pages for forms.
To me, this only make sense if you don't have many interactions (comments) and if the website isn't updated 300 times/day. But it is a nice solution.
First, security, particularly compared to wordpress.
Second, you can host the resulting HTML anywhere, for instance, a subdirectory of a web server you don't want to write a blog engine for. my corporate site is powered by Nitrogen (Erlang) and I just whipped out a Jekyll template this week for the blog we're adding - then we can host the blog under that site without having to go write a blog framework in Erlang.
The "configuration" is a Haskell program that uses the Hakyll library as a DSL.
I use it for my home page: http://chrisdone.com/
Once I learn enough Sinatra to build a user creation / login system similar to Wishlist Member, I'll never use Wordpress again.