Ask HN: Managed web hosting as a service, in 2019?

I'm building an app for a prosumer niche and I want to offer a "white label" feature. I realized that this would essentially boil down to a form of managed web hosting. Users would set their CNAME or A domain records to point at my app, and have the ability to git push a statically served repository.

Potentially, my app would "inject" or connect some extras in the process. An example would be linking in a library that exposes a JS event API, or have defaults that would get served in case a path is not present in the repo. The repositories would get served like an AWS S3 static website and scale based on demand. Another option would be static container images built on each push, like a CI process.

Seems like this is a problem that would warrant a generic solution, as it would be useful in many niches.

Are there any services out there that already do this? How would you approach building a feature like this today? Any pitfalls to avoid?

Essentially, I think I'm looking for something like a cheap hybrid between now.sh or Squarespace in-a-box, offered as a service...