But...SSG is how pages traditionally worked. You have some files in a folder and use <a> to link between them, no dedicated router required. Routers are needed in SSR though, depending on your use case.
SSG in Next vocabulary (which I employ because Perseus claims to be a Next alternative) is prerendering a page at build-time, not necessarily the whole site. So Next will still allow client-side routing, with its hybrid approach. What you describe is an exported app, sometimed named SPA (the name is wrong but people get the point), MPA or static app.
And traditionally it was limited so different expectations. If you needed more you'd use PHP or something else. Problem here as other commenters have mentioned is how the line between SSR, SSG and others have been blurred.
We're now given something that has routing i.e. NextJs but then allowed a SSG option that behaves somewhat different.
It's good if your platform can support it.