I mean the framework can of course differientiate those use cases clearly, static and dynamic still exist in Next 13 App Router. But making them totally separate is a mistake too. Namely what bothers me is that a few points made in the docs or by users in this comment section show a limited visions of static rendering. It is certainly not limited to generic content that is the same for all users, I've built enough counter-examples to prove it.
Why is it a mistake to separate them? If can generate my site as a bunch of static content, upload it to a server, and have it served by nginx or similar, then I don't need to think about the next.js App Router, React, or indeed any custom server-side code. That's what static site generation is for, and it seems rather distinct from what you are talking about.
Yes it is limiting, and it won't be appropriate for many use cases. But if you can do it, it makes things simpler, cheaper and more efficient.
That's not to say you can't combine SSG tooling with dynamic content too if you need it. But static-only is a perfectly valid choice if you can get away with it.
Your answer conflates statically rendering a page (server-side prerendering at build-time), and statically rendering a website (exporting in Next.js terminology). You seem to talk about statically rendering the website while my point is more about statically rendering pages or layouts.
