Something I have yet to see but that I think would be perfect would be a client-side single-page-app that served as a s3-backed static site generator.
Navigate to MyStaticWebsiteGenerator.io (or download it, or self-host it, or clone the repo, it's a simple js-based SPA preferably packaged as a stand-alone ".html" file). AWS credentials (IAM of course) are either stored encrypted in LocalStorage (or Websql or indexeddb or who knows what we are supposed to be using) or queried on demand. It would interact with s3 directly (there is a browser based js api for aws) to manage and modify files directly (multi-user contention and eventual consistency be damned - for small sites it's simply not an issue), and when appropriate, generate/regenerate the static files. Because everything is done client side, the webserver itself never sees or cares about your aws credentials.
Clearly, being a "static site generator", only the admin interface would be JS based, the user-facing generated content would be static. [For some reason every post i've seen doing something remotely similar wants their mostly static content to be rendered at runtime in their js app???]
With prosemirror under active development you should soon be able to have a simple js based WYSIWYG rich text editor that generates nice clean Markdown to feed into your template of choice (à la Jekyll). Your end-users don't need to know markdown or care, they just get a fairly basic rich text editor. Give them a simple interface for defining a website's structure and bob's your uncle.
Sometimes I feel like I'm the only person who thinks this way.
Me either but I'm considering using Ghost (which does have a nice frontend) and liberating the content from the SQLite database into static files for generation and serving.
Could be. Content and templates could be hosted on S3. Unfortunately I haven't found a good admin GUI for a static site generator yet. I use Jekyll myself and as a developer that's great, not something I would recommend to normal users though. Which is a shame because most users (or small businesses) don't really have such complex requirements. Most don't really need their site to be dynamic, and what requires some server functionality can be solved with an external service (save data, send email etc).