In my experience moving-fast SSR absolutely does leave behind a wake of idiosyncratic APIs that definitely need to be cleaned up later.
You still need client-server communication, so you still have an API, it's just an ad hoc API that speaks HTML and form data instead of JSON. And because you didn't think of it as an API while you were building it, it actually tends to be harder to clean up later, not easier.
You probably have more experience than me. My primary SSR experience is with more recent frameworks and libraries like blitz and tRPC, which make it much easier to delete those when they are no longer used.
You still need client-server communication, so you still have an API, it's just an ad hoc API that speaks HTML and form data instead of JSON. And because you didn't think of it as an API while you were building it, it actually tends to be harder to clean up later, not easier.