Getting an API for free is an anti-feature for all the temporarily-embarrassed monopolists on HN.
More seriously, though, it's nice to be able to just build without thinking too hard about if you're getting your abstractions perfect. To me, this is the main advantage of SSR - moving fast doesn't leave behind a wake of idiosyncratic APIs that need to be (carefully, dangerously) cleaned up later.
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.
More seriously, though, it's nice to be able to just build without thinking too hard about if you're getting your abstractions perfect. To me, this is the main advantage of SSR - moving fast doesn't leave behind a wake of idiosyncratic APIs that need to be (carefully, dangerously) cleaned up later.