>Nobody said doing an API-based design requires you to (purely) client-side render.

And if you go down that route, you pay for the increased deployment and maintenance complexity as well as the RTT to call the API service and consume the response as well as the CPU cost to render the page. There's no free lunch here. You can have both the API and rendering service on the same box, but now it's looking less and less clean and tidy, and more and more like a traditional web-app.