You just described Movable Type (https://movabletype.org/), which was WordPress before WordPress was WordPress.
The irony here is that the reason WordPress eclipsed Movable Type was that people got tired of having to go through the edit-output static files-publish cycle to modify their content. They wanted to make their changes in an editor and have them appear immediately on the live site, without waiting for a new set of static files to grind out. WP, which generates all pages dynamically, met that demand nicely.
Then of course people eventually discovered the downside of generating every page dynamically, namely that it's much more resource intensive, and started to clamor for something more efficient. So the current wave of static site generators were born, doing the exact same thing MT got killed in the marketplace for doing.
Yeah, I learned about MT's approach from Jeff Atwood back in '09, and have been reading about the new "discovery" of the static site generators with some amusement.
That said, MT has a big issue: for something that has been killed in the marketplace, it's quite expensive. I'd love to use it for the non-profit I help out, but at a $1000, it's about $950 more than what they can aford.
The last time I used WordPress (fortunately, very long ago) the most popular caching strategies were SuperCache (writes HTML files to the webroot) and Varnish (a caching reverse-proxy.) In both cases it's trivial to separate the static content from the administrative area. I don't recommend this (I don't recommend anything WordPress) but that seems like what the poster is asking for.
Does this exist?