Ability to link to documents, bookmark, meaningfully use history and save pages to the disk for offline use. Ability of the users to customize standard behaviors without reverse-engineering your JavaScript code. Transparency, which often leads to much, much easier debugging and improved usability. No need to run a quad-core 4GB desktop to use the website.
And this is just the stuff relevant to internal (non-public) websites. You can argue that all of this can be achieved with JavaScript heavy clients, but in reality, it's just isn't. It's not something you get by default, it's tons of extra work, and most people don't do that work.
Even just in principle, it can't possibly be close to as fast (client-side can render optimistically, where possible), and it can't be close to as flexible (you don't have a model of state on the client to perform logic with).
In principle, server-side rendering can allow you to share pre-rendered components between thousands of users saving everyone tons of work. In practice, rendering on the server side is just string concatenation and is insignificant compared to things like running SQL quires, which you'll have to do anyway.