The reason client-side rendering is so popular (IME) is that it creates a clear separation between frontend and backend devs. You can use separate repositories, languages, deployment flows/cadences, code review, etc, with an API as your connection point (and the fact that you get an API by default with CSR is also nice). I don't think CSR is going anywhere, mainly thanks to Conway's Law.
The same argument could be used for splitting backend to multiple services, or even micro services. Frontend/backend separation seems pretty arbitrary. If anything, I'd say that with server rendering, separating different modules is easier. You want to rewrite that page? No problems. With client-side rendering there's usually expectation of some monolith project using the single framework.
1. Written in different languages.
2. Completely different deployment paths.
3. Causing completely different ways of scaling.
4. Focus on UI and UX is a very different mindset, with often some people preferring it to be a focus of their work, or not.