The project I work on, Netlify CMS (https://www.netlifycms.org/), is almost precisely what you described in your last paragraph.I say "only" because it only officially supports GitHub as a backend at the moment, from which you can deploy to a host. (I'm also currently working on supporting more backends, so that will change soon.) The CMS is an open-source (MIT license) CMS built as a static web page which connects to an API for an arbitrary backend from your browser and edits the content stored there - from there, you can build the content with whatever static site generator you want. This lets you build sites that non-technical users can keep up-to-date without tying yourself to a specific tech stack for the actual website.
(disclaimer: Netlify employee)