This is fairly reductive. SSR is less about rendering HTML on the server, and more about having both the initial render and the client-side updates use the same process. Contrast this with other ways of rendering the front-end where either the client needs to build the entire view itself, or you need to write a separate application to do any client-side manipulation that might be necessary.

As with everything in software, it's all about tradeoffs. Using PHP to render your templates works great if there's limited client-side interaction (say, blogs, forums, documents, marketing pages etc), while frontend rendering allows you to build much more complicated applications that can react much quicker to user interaction, but will be slower to load the more complicated they become. And SSR tools try and have the best of both worlds, but make other aspects more complex in exchange.