I think you're misunderstanding what Wordpress's static site generator plugin does. It bakes the WP content in to static HTML files that the server (eg nginx) then serves to the user. Website visitors never hit any part of WP. It's only there for the admin and editor. You can serve the static files from a different server infrastructure (say, an S3 bucket) with a little work.
In other words, it does precisely what you're saying it should do.
You only have to maintain the Wordpress site unless you do fancy stuff on top of it. And on modern Wordpress that's quite minimal. The point of this approach is that people with Wordpress expertise can continue to manage the website and you get all the benefits of a static website.
In other words, it does precisely what you're saying it should do.