People are looking to static sites more and more for a couple of reasons:
1. speed - you can't beat an optimized static sites hosted on a CDN. In part I suppose the increased focus on speed i driven by mobile traffic.
2. Github - front-end developers have now gotten really used to having everything under version control. Dumping the most important content into an unversioned database just doesn't feel as good as having everything as Markdown in Github
3. Jekyll - or rather build tools and static site generators in general. The combination of GitHub and Jekyll and flag ship projects such as the Obama Campaign platform [1] definitively played an essential role in the growth of static site generators we're seeing now.
Our clients range from beginners launching their very first HTML site, over agencies with really cool flows built around Middlemand/GitHub/Draft/Similar services, to companies that are integrating site publishing into their products in various forms.
One of the cool examples is a startup doing a site builder for progressive candidates running for national campaigns. They use our API to handle the publishing, and use our form feature for gathering volunteer submissions and contact mails.
In general I think publishing a website with a form on it, is one of the most basic features of the web. Making it faster, easier and better is a pretty obvious plus for a lot of people.
Basically, I build static sites for some small businesses in the area. They want to be able to choose where everything goes, to the pixel, so it's easiest to work with just html and css. Then I can upload to BitBalloon and everything works exactly as it did on my laptop. Forms work, everything gets optimized, and setting up my own domains is super simple. And it's cheap.
I could use S3 or something else, and it would be cheaper, but deploying in a half second really is useful. Everything is done right with no effort on my part other than building the site itself.
I also built a site just for fun and host it there. 750,000 page views in the last couple weeks, didn't worry for a second. http://gallerrit.com/ It has also been very easy to push updated versions with no down time.
(or, better asked: what is the problem these solutions solve?)