I think most importantly the server can cache requests (cache the generated HTML). This is especially important for public, mostly static pages that one might want to do SEO optimizations for anyways.
Servers are often weaker than many consumer computers anyways, so I don’t thin it’s because it can render faster than your own browser.
I don't think the purpose of SSR + hydration is to simply move the wait time from first render to server response, or that servers can somehow render faster. To fully yield the benefits you'd have to enable caching, so that the server spits out something without rendering and the client side can simply hydrate.
Caching is not something individual distributed clients can do, which is why the server is the only way able to reasonably take on this role. You can also easily configure nginx to serve just-in-time caching.
Servers are often weaker than many consumer computers anyways, so I don’t thin it’s because it can render faster than your own browser.