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

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.