And with a host like Surge or Netlify you can run an entire site for just the cost of a domain name.
The closest I've seen is using Sandstorm with their static Wordpress site publishing but it's still nowhere near as smooth as plain Wordpress.
(Edit: let's add some qualification because downvoting)
When I first started using static sites I would have agreed with you: there's no way I'd hand a normal user a markdown editor and a git repo and expect them to get on with it. But these new services do, in my opinion, solve the experience problem.
However Wordpress is really good if you want to leverage the module ecosystem and do more complex stuff further down the line.
Having used Wordpress for years I get excited about static sites' speed, simplicity and lack of constant security updates but it's not a one size fits all situation.
Forestry.io is a Git-based CMS that commits content changes to your repo (and optionally builds/deploys your site). Contentful is an API-based CMS, that stores your content and requires you to query their API during/after build time.
So you would use Forestry if you're hosting static HTML from CMS, and Contentful for when you need an API for the CMS.
(disclamer: I've never used CMS before so I don't really know how it works)